diff --git a/bindings/pydrake/solvers/BUILD.bazel b/bindings/pydrake/solvers/BUILD.bazel
index 30cfc9dc7e9e..bb288c3cfad7 100644
--- a/bindings/pydrake/solvers/BUILD.bazel
+++ b/bindings/pydrake/solvers/BUILD.bazel
@@ -46,6 +46,7 @@ drake_pybind_library(
         "//bindings/pydrake:symbolic_types_pybind",
         "//bindings/pydrake/common:cpp_param_pybind",
         "//bindings/pydrake/common:cpp_template_pybind",
+        "//bindings/pydrake/common:deprecation_pybind",
         "//bindings/pydrake/common:eigen_pybind",
         "//bindings/pydrake/common:value_pybind",
     ],
@@ -173,7 +174,7 @@ drake_py_unittest(
     }),
     deps = [
         ":solvers",
-        "//bindings/pydrake/common/test_utilities:numpy_compare_py",
+        "//bindings/pydrake/common/test_utilities",
     ],
 )
 
diff --git a/bindings/pydrake/solvers/solvers_py_dreal.cc b/bindings/pydrake/solvers/solvers_py_dreal.cc
index 8cd42dd2e748..47c8536cd89b 100644
--- a/bindings/pydrake/solvers/solvers_py_dreal.cc
+++ b/bindings/pydrake/solvers/solvers_py_dreal.cc
@@ -2,6 +2,7 @@
 #include "pybind11/pybind11.h"
 #include "pybind11/stl.h"
 
+#include "drake/bindings/pydrake/common/deprecation_pybind.h"
 #include "drake/bindings/pydrake/documentation_pybind.h"
 #include "drake/bindings/pydrake/pydrake_pybind.h"
 #include "drake/bindings/pydrake/solvers/solvers_py.h"
@@ -11,21 +12,26 @@ namespace drake {
 namespace pydrake {
 namespace internal {
 
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
 void DefineSolversDreal(py::module m) {
   // NOLINTNEXTLINE(build/namespaces): Emulate placement in namespace.
   using namespace drake::solvers;
   constexpr auto& doc = pydrake_doc.drake.solvers;
 
   auto solver = py::class_<DrealSolver, SolverInterface>(
-      m, "DrealSolver", doc.DrealSolver.doc)
-                    .def_static("id", &DrealSolver::id, doc.DrealSolver.id.doc);
+      m, "DrealSolver", doc.DrealSolver.doc_deprecated)
+                    .def_static("id",
+                        WrapDeprecated(doc.DrealSolver.id.doc_deprecated,
+                            &DrealSolver::id),
+                        doc.DrealSolver.id.doc_deprecated);
 
   {
     using Class = DrealSolver::Interval;
     const auto& cls_doc = doc.DrealSolver.Interval;
-    py::class_<Class>(solver, "Interval", cls_doc.doc)
-        .def(py::init<double, double>(), py::arg("low"), py::arg("high"),
-            cls_doc.ctor.doc)
+    py::class_<Class>(solver, "Interval", cls_doc.doc_deprecated)
+        .def(py_init_deprecated<Class, double, double>(cls_doc.doc_deprecated),
+            py::arg("low"), py::arg("high"), cls_doc.doc_deprecated)
         .def("diam", &Class::diam, cls_doc.diam.doc)
         .def("mid", &Class::mid, cls_doc.mid.doc)
         .def("low", &Class::low, cls_doc.low.doc)
@@ -40,14 +46,22 @@ void DefineSolversDreal(py::module m) {
         .value("kNotUse", Class::kNotUse, cls_doc.kNotUse.doc);
   }
 
-  solver.def(py::init<>(), doc.DrealSolver.ctor.doc)
-      .def_static("CheckSatisfiability", &DrealSolver::CheckSatisfiability,
+  solver
+      .def(py_init_deprecated<DrealSolver>(doc.DrealSolver.ctor.doc_deprecated),
+          doc.DrealSolver.ctor.doc_deprecated)
+      .def_static("CheckSatisfiability",
+          WrapDeprecated(doc.DrealSolver.CheckSatisfiability.doc_deprecated,
+              &DrealSolver::CheckSatisfiability),
           py::arg("f"), py::arg("delta"),
-          doc.DrealSolver.CheckSatisfiability.doc)
-      .def_static("Minimize", &DrealSolver::Minimize, py::arg("objective"),
-          py::arg("constraint"), py::arg("delta"),
-          py::arg("local_optimization"), doc.DrealSolver.Minimize.doc);
+          doc.DrealSolver.CheckSatisfiability.doc_deprecated)
+      .def_static("Minimize",
+          WrapDeprecated(
+              doc.DrealSolver.Minimize.doc_deprecated, &DrealSolver::Minimize),
+          py::arg("objective"), py::arg("constraint"), py::arg("delta"),
+          py::arg("local_optimization"),
+          doc.DrealSolver.Minimize.doc_deprecated);
 }
+#pragma GCC diagnostic pop
 
 }  // namespace internal
 }  // namespace pydrake
diff --git a/bindings/pydrake/solvers/solvers_py_ibex.cc b/bindings/pydrake/solvers/solvers_py_ibex.cc
index da4c99618acf..32a069b61637 100644
--- a/bindings/pydrake/solvers/solvers_py_ibex.cc
+++ b/bindings/pydrake/solvers/solvers_py_ibex.cc
@@ -1,6 +1,7 @@
 #include "pybind11/eigen.h"
 #include "pybind11/pybind11.h"
 
+#include "drake/bindings/pydrake/common/deprecation_pybind.h"
 #include "drake/bindings/pydrake/documentation_pybind.h"
 #include "drake/bindings/pydrake/pydrake_pybind.h"
 #include "drake/bindings/pydrake/solvers/solvers_py.h"
@@ -10,15 +11,22 @@ namespace drake {
 namespace pydrake {
 namespace internal {
 
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
 void DefineSolversIbex(py::module m) {
   // NOLINTNEXTLINE(build/namespaces): Emulate placement in namespace.
   using namespace drake::solvers;
   constexpr auto& doc = pydrake_doc.drake.solvers;
 
-  py::class_<IbexSolver, SolverInterface>(m, "IbexSolver", doc.IbexSolver.doc)
-      .def(py::init<>(), doc.IbexSolver.ctor.doc)
-      .def_static("id", &IbexSolver::id, doc.IbexSolver.id.doc);
+  py::class_<IbexSolver, SolverInterface>(
+      m, "IbexSolver", doc.IbexSolver.doc_deprecated)
+      .def(py_init_deprecated<IbexSolver>(doc.IbexSolver.ctor.doc_deprecated),
+          doc.IbexSolver.ctor.doc_deprecated)
+      .def_static("id",
+          WrapDeprecated(doc.IbexSolver.id.doc_deprecated, &IbexSolver::id),
+          doc.IbexSolver.id.doc_deprecated);
 }
+#pragma GCC diagnostic pop
 
 }  // namespace internal
 }  // namespace pydrake
diff --git a/bindings/pydrake/solvers/solvers_py_mathematicalprogram.cc b/bindings/pydrake/solvers/solvers_py_mathematicalprogram.cc
index c582c448ca6a..49a3f0e05fb2 100644
--- a/bindings/pydrake/solvers/solvers_py_mathematicalprogram.cc
+++ b/bindings/pydrake/solvers/solvers_py_mathematicalprogram.cc
@@ -458,14 +458,13 @@ void BindSolverInterfaceAndFlags(py::module m) {
       .value("kLCP", ProgramType::kLCP, doc.ProgramType.kLCP.doc)
       .value("kUnknown", ProgramType::kUnknown, doc.ProgramType.kUnknown.doc);
 
-  py::enum_<SolverType>(m, "SolverType", doc.SolverType.doc)
+  py::enum_<SolverType> solver_type(m, "SolverType", doc.SolverType.doc);
+  solver_type  // BR
       .value("kClp", SolverType::kClp, doc.SolverType.kClp.doc)
       .value("kCsdp", SolverType::kCsdp, doc.SolverType.kCsdp.doc)
-      .value("kDReal", SolverType::kDReal, doc.SolverType.kDReal.doc)
       .value("kEqualityConstrainedQP", SolverType::kEqualityConstrainedQP,
           doc.SolverType.kEqualityConstrainedQP.doc)
       .value("kGurobi", SolverType::kGurobi, doc.SolverType.kGurobi.doc)
-      .value("kIbex", SolverType::kIbex, doc.SolverType.kIbex.doc)
       .value("kIpopt", SolverType::kIpopt, doc.SolverType.kIpopt.doc)
       .value("kLinearSystem", SolverType::kLinearSystem,
           doc.SolverType.kLinearSystem.doc)
@@ -476,6 +475,13 @@ void BindSolverInterfaceAndFlags(py::module m) {
       .value("kScs", SolverType::kScs, doc.SolverType.kScs.doc)
       .value("kSnopt", SolverType::kSnopt, doc.SolverType.kSnopt.doc);
 
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
+  solver_type  // BR
+      .value("kDReal", SolverType::kDReal, "(Deprecated.)")
+      .value("kIbex", SolverType::kIbex, "(Deprecated.)");
+#pragma GCC diagnostic pop
+
   // TODO(jwnimmer-tri) Bind the accessors for SolverOptions.
   py::class_<SolverOptions>(m, "SolverOptions", doc.SolverOptions.doc)
       .def(py::init<>(), doc.SolverOptions.ctor.doc)
diff --git a/bindings/pydrake/solvers/test/dreal_solver_test.py b/bindings/pydrake/solvers/test/dreal_solver_test.py
index acf3f0259f25..971a1c0c9e25 100644
--- a/bindings/pydrake/solvers/test/dreal_solver_test.py
+++ b/bindings/pydrake/solvers/test/dreal_solver_test.py
@@ -4,6 +4,7 @@
 import numpy as np
 
 from pydrake.common.containers import EqualToDict
+from pydrake.common.test_utilities.deprecation import catch_drake_warnings
 from pydrake.solvers import mathematicalprogram as mp
 from pydrake.solvers.dreal import DrealSolver
 from pydrake.symbolic import Variable, logical_and, logical_or
@@ -15,8 +16,11 @@ def test_dreal_solver(self):
         prog = mp.MathematicalProgram()
         x = prog.NewContinuousVariables(1, "x")
         prog.AddBoundingBoxConstraint(-1, 1, x)
-        solver = DrealSolver()
-        self.assertEqual(solver.solver_id(), DrealSolver.id())
+        with catch_drake_warnings(expected_count=1):
+            solver = DrealSolver()
+        with catch_drake_warnings(expected_count=1):
+            dreal_id = DrealSolver.id()
+        self.assertEqual(solver.solver_id(), dreal_id)
         self.assertTrue(solver.available())
         self.assertEqual(solver.solver_id().name(), "dReal")
         self.assertEqual(solver.SolverName(), "dReal")
@@ -25,7 +29,8 @@ def test_dreal_solver(self):
         self.assertTrue(result.is_success())
 
     def test_interval(self):
-        interval = DrealSolver.Interval(low=3.0, high=4.0)
+        with catch_drake_warnings(expected_count=1):
+            interval = DrealSolver.Interval(low=3.0, high=4.0)
         self.assertEqual(interval.low(), 3.0)
         self.assertEqual(interval.high(), 4.0)
         self.assertEqual(interval.diam(), 1.0)
@@ -34,8 +39,9 @@ def test_interval(self):
     def test_dreal_satisfiability(self):
         x = Variable("x")
         f = logical_and(x > 1, x < 2)
-        interval_box = EqualToDict(
-            DrealSolver.CheckSatisfiability(f=f, delta=0.01))
+        with catch_drake_warnings(expected_count=1):
+            interval_box = EqualToDict(
+                DrealSolver.CheckSatisfiability(f=f, delta=0.01))
         self.assertEqual(len(interval_box), 1)
         self.assertIsInstance(interval_box[x], DrealSolver.Interval)
 
@@ -47,12 +53,13 @@ def test_local_optimization(self):
     def test_minimize(self):
         x = Variable("x")
         delta = 0.01
-        interval_box = EqualToDict(
-            DrealSolver.Minimize(
-                objective=x**2,
-                constraint=logical_and(x >= 1, x <= 10),
-                delta=delta,
-                local_optimization=DrealSolver.LocalOptimization.kUse))
+        with catch_drake_warnings(expected_count=1):
+            interval_box = EqualToDict(
+                DrealSolver.Minimize(
+                    objective=x**2,
+                    constraint=logical_and(x >= 1, x <= 10),
+                    delta=delta,
+                    local_optimization=DrealSolver.LocalOptimization.kUse))
         self.assertEqual(len(interval_box), 1)
         self.assertIsInstance(interval_box[x], DrealSolver.Interval)
         print(interval_box[x].diam())
@@ -60,5 +67,6 @@ def test_minimize(self):
 
     def unavailable(self):
         """Per the BUILD file, this test is only run when dReal is disabled."""
-        solver = DrealSolver()
+        with catch_drake_warnings(expected_count=1):
+            solver = DrealSolver()
         self.assertFalse(solver.available())
diff --git a/bindings/pydrake/solvers/test/ibex_solver_test.py b/bindings/pydrake/solvers/test/ibex_solver_test.py
index 759b513e8306..083681bbe109 100644
--- a/bindings/pydrake/solvers/test/ibex_solver_test.py
+++ b/bindings/pydrake/solvers/test/ibex_solver_test.py
@@ -3,6 +3,7 @@
 import numpy as np
 
 from pydrake.common.test_utilities import numpy_compare
+from pydrake.common.test_utilities.deprecation import catch_drake_warnings
 from pydrake.solvers import mathematicalprogram as mp
 from pydrake.solvers.ibex import IbexSolver
 
@@ -14,8 +15,11 @@ def test_ibex_solver(self):
         prog.AddBoundingBoxConstraint(-1., 1., x[0])
         prog.AddBoundingBoxConstraint(-1., 1., x[1])
         prog.AddCost(x[0] - x[1])
-        solver = IbexSolver()
-        self.assertEqual(solver.solver_id(), IbexSolver.id())
+        with catch_drake_warnings(expected_count=1):
+            solver = IbexSolver()
+        with catch_drake_warnings(expected_count=1):
+            ibex_id = IbexSolver.id()
+        self.assertEqual(solver.solver_id(), ibex_id)
 
         self.assertTrue(solver.available())
         self.assertEqual(solver.solver_id().name(), "IBEX")
@@ -29,5 +33,6 @@ def test_ibex_solver(self):
 
     def unavailable(self):
         """Per the BUILD file, this test is only run when Ibex is disabled."""
-        solver = IbexSolver()
+        with catch_drake_warnings(expected_count=1):
+            solver = IbexSolver()
         self.assertFalse(solver.available())
diff --git a/solvers/BUILD.bazel b/solvers/BUILD.bazel
index 7040e1d96316..5b48947b207b 100644
--- a/solvers/BUILD.bazel
+++ b/solvers/BUILD.bazel
@@ -1294,6 +1294,7 @@ drake_cc_googletest(
 drake_cc_googletest(
     name = "dreal_solver_test",
     timeout = "moderate",
+    copts = ["-Wno-deprecated-declarations"],
     # For most of floating-point operations, Valgrind core only supports the
     # IEEE default mode (round to nearest) while dReal uses to +infinity
     # and to -infinity rounding modes intensively to maintain conservative
@@ -1348,6 +1349,7 @@ drake_cc_googletest(
 
 drake_cc_googletest(
     name = "ibex_solver_test",
+    copts = ["-Wno-deprecated-declarations"],
     deps = [
         ":generic_trivial_constraint",
         ":generic_trivial_cost",
diff --git a/solvers/dreal_solver.cc b/solvers/dreal_solver.cc
index f0fb52098f2c..e7f1a984e538 100644
--- a/solvers/dreal_solver.cc
+++ b/solvers/dreal_solver.cc
@@ -16,6 +16,9 @@
 #include "drake/common/text_logging.h"
 #include "drake/solvers/mathematical_program.h"
 
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
+
 namespace drake {
 namespace solvers {
 
@@ -603,3 +606,5 @@ void DrealSolver::DoSolve(
 
 }  // namespace solvers
 }  // namespace drake
+
+#pragma GCC diagnostic pop
diff --git a/solvers/dreal_solver.h b/solvers/dreal_solver.h
index 2d578fcc4a6d..e478579689a1 100644
--- a/solvers/dreal_solver.h
+++ b/solvers/dreal_solver.h
@@ -5,6 +5,7 @@
 #include <unordered_map>
 
 #include "drake/common/drake_copyable.h"
+#include "drake/common/drake_deprecated.h"
 #include "drake/common/hash.h"
 #include "drake/common/symbolic/expression.h"
 #include "drake/solvers/solver_base.h"
@@ -12,28 +13,26 @@
 namespace drake {
 namespace solvers {
 
+/// (Deprecated.) dReal support is being withdrawn from Drake; for details, see
+/// https://github.com/RobotLocomotion/drake/pull/18156. This class will be
+/// removed from Drake on or after 2023-02-01.
+///
 /// An implementation of SolverInterface for the dReal4 solver
 /// (https://github.com/dreal/dreal4).
-///
-/// Currently this implementation supports the following options:
-///  * precision <double>: This value is used as a termination condition. When
-///                        the ICP algorithm finds an interval box whose width
-///                        is smaller than this value, it concludes that the
-///                        query is delta-satisfiable and provides the interval
-///                        box as a witness. Default value = 0.001.
-///
-///  * use_local_optimization <bool>: Use local-optimization algorithms in
-///                                   solving exists-forall problem. For now,
-///                                   the solver is using NLopt. See
-///                                   https://link.springer.com/chapter/10.1007%2F978-3-319-96142-2_15
-///                                   for details. Default value = True.
-///
-/// To see the full list of dReal4 options, visit
-/// https://github.com/dreal/dreal4#command-line-options.
-class DrealSolver final : public SolverBase {
+class DRAKE_DEPRECATED("2023-02-01",
+    "dReal support is being withdrawn from Drake; for details, see "
+    "https://github.com/RobotLocomotion/drake/pull/18156")
+DrealSolver final : public SolverBase {
  public:
+  /// (Deprecated.) dReal support is being withdrawn from Drake; for details,
+  /// see https://github.com/RobotLocomotion/drake/pull/18156. This class will
+  /// be removed from Drake on or after 2023-02-01.
+  ///
   /// Class representing an interval of doubles.
-  class Interval {
+  class DRAKE_DEPRECATED("2023-02-01",
+      "dReal support is being withdrawn from Drake; for details, see "
+      "https://github.com/RobotLocomotion/drake/pull/18156")
+  Interval {
    public:
     DRAKE_DEFAULT_COPY_AND_MOVE_AND_ASSIGN(Interval)
 
@@ -62,9 +61,17 @@ class DrealSolver final : public SolverBase {
     double high_{};
   };
 
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
+  /// (Deprecated.) dReal support is being withdrawn from Drake; for details,
+  /// see https://github.com/RobotLocomotion/drake/pull/18156. This class will
+  /// be removed from Drake on or after 2023-02-01.
   using IntervalBox = std::unordered_map<symbolic::Variable, Interval>;
+#pragma GCC diagnostic pop
 
-  /// Indicates whether to use dReal's --local-optimization option or not.
+  /// (Deprecated.) dReal support is being withdrawn from Drake; for details,
+  /// see https://github.com/RobotLocomotion/drake/pull/18156. This class will
+  /// be removed from Drake on or after 2023-02-01.
   enum class LocalOptimization {
     kUse,     ///< Use "--local-optimization" option.
     kNotUse,  ///< Do not use "--local-optimization" option.
@@ -72,28 +79,23 @@ class DrealSolver final : public SolverBase {
 
   DRAKE_NO_COPY_NO_MOVE_NO_ASSIGN(DrealSolver)
 
+  DRAKE_DEPRECATED("2023-02-01",
+      "dReal support is being withdrawn from Drake; for details, see "
+      "https://github.com/RobotLocomotion/drake/pull/18156")
   DrealSolver();
+
   ~DrealSolver() final;
 
-  /// Checks the satisfiability of a given formula @p f with a given precision
-  /// @p delta.
-  ///
-  /// @returns a model, a mapping from a variable to an interval, if @p f is
-  /// δ-satisfiable.
-  /// @returns a nullopt, if @p is unsatisfiable.
+  DRAKE_DEPRECATED("2023-02-01",
+      "dReal support is being withdrawn from Drake; for details, see "
+      "https://github.com/RobotLocomotion/drake/pull/18156")
   static std::optional<IntervalBox> CheckSatisfiability(
       const symbolic::Formula& f,
       double delta);
 
-  /// Finds a solution to minimize @p objective function while satisfying a
-  /// given @p constraint using @p delta. When @p local_optimization is
-  /// Localoptimization::kUse, enable "--local-optimization" dReal option which
-  /// uses NLopt's local-optimization algorithms to refine counterexamples in
-  /// the process of global optimization.
-  ///
-  /// @returns a model, a mapping from a variable to an interval, if a solution
-  /// exists.
-  /// @returns nullopt, if there is no solution.
+  DRAKE_DEPRECATED("2023-02-01",
+      "dReal support is being withdrawn from Drake; for details, see "
+      "https://github.com/RobotLocomotion/drake/pull/18156")
   static std::optional<IntervalBox> Minimize(
       const symbolic::Expression& objective,
       const symbolic::Formula& constraint,
@@ -102,9 +104,21 @@ class DrealSolver final : public SolverBase {
 
   /// @name Static versions of the instance methods with similar names.
   //@{
+  DRAKE_DEPRECATED("2023-02-01",
+      "dReal support is being withdrawn from Drake; for details, see "
+      "https://github.com/RobotLocomotion/drake/pull/18156")
   static SolverId id();
+  DRAKE_DEPRECATED("2023-02-01",
+      "dReal support is being withdrawn from Drake; for details, see "
+      "https://github.com/RobotLocomotion/drake/pull/18156")
   static bool is_available();
+  DRAKE_DEPRECATED("2023-02-01",
+      "dReal support is being withdrawn from Drake; for details, see "
+      "https://github.com/RobotLocomotion/drake/pull/18156")
   static bool is_enabled();
+  DRAKE_DEPRECATED("2023-02-01",
+      "dReal support is being withdrawn from Drake; for details, see "
+      "https://github.com/RobotLocomotion/drake/pull/18156")
   static bool ProgramAttributesSatisfied(const MathematicalProgram&);
   //@}
 
diff --git a/solvers/dreal_solver_common.cc b/solvers/dreal_solver_common.cc
index 0bdd586f8643..703783204965 100644
--- a/solvers/dreal_solver_common.cc
+++ b/solvers/dreal_solver_common.cc
@@ -8,6 +8,9 @@
 // This file contains implementations that are common to both the available and
 // unavailable flavor of this class.
 
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
+
 namespace drake {
 namespace solvers {
 
@@ -41,3 +44,5 @@ bool DrealSolver::ProgramAttributesSatisfied(const MathematicalProgram& prog) {
 
 }  // namespace solvers
 }  // namespace drake
+
+#pragma GCC diagnostic pop
diff --git a/solvers/ibex_solver.cc b/solvers/ibex_solver.cc
index 1d1a4e632cf9..d3c9b7cc4075 100644
--- a/solvers/ibex_solver.cc
+++ b/solvers/ibex_solver.cc
@@ -10,6 +10,9 @@
 #include "drake/common/text_logging.h"
 #include "drake/solvers/ibex_converter.h"
 
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
+
 namespace drake {
 namespace solvers {
 
@@ -373,3 +376,5 @@ void IbexSolver::DoSolve(const MathematicalProgram& prog,
 
 }  // namespace solvers
 }  // namespace drake
+
+#pragma GCC diagnostic pop
diff --git a/solvers/ibex_solver.h b/solvers/ibex_solver.h
index 7e532685f65f..20b5bbc5e757 100644
--- a/solvers/ibex_solver.h
+++ b/solvers/ibex_solver.h
@@ -1,6 +1,7 @@
 #pragma once
 
 #include "drake/common/drake_copyable.h"
+#include "drake/common/drake_deprecated.h"
 #include "drake/solvers/mathematical_program.h"
 #include "drake/solvers/mathematical_program_result.h"
 #include "drake/solvers/solver_base.h"
@@ -8,6 +9,10 @@
 
 namespace drake {
 namespace solvers {
+/// (Deprecated.) IBEX support is being withdrawn from Drake; for details, see
+/// https://github.com/RobotLocomotion/drake/pull/18156. This class will be
+/// removed from Drake on or after 2023-02-01.
+///
 /// An implementation of SolverInterface for the IBEX solver
 /// (http://www.ibex-lib.org).
 ///
@@ -41,11 +46,18 @@ namespace solvers {
 ///  - timeout <double>: Timeout (time in seconds). 0.0 indicates +∞.
 ///
 /// See http://www.ibex-lib.org/doc/optim.html#options for more information.
-class IbexSolver final : public SolverBase {
+class DRAKE_DEPRECATED("2023-02-01",
+    "IBEX support is being withdrawn from Drake; for details, see "
+    "https://github.com/RobotLocomotion/drake/pull/18156")
+IbexSolver final : public SolverBase {
  public:
   DRAKE_NO_COPY_NO_MOVE_NO_ASSIGN(IbexSolver)
 
+  DRAKE_DEPRECATED("2023-02-01",
+      "IBEX support is being withdrawn from Drake; for details, see "
+      "https://github.com/RobotLocomotion/drake/pull/18156")
   IbexSolver();
+
   ~IbexSolver() final;
 
   // A using-declaration adds these methods into our class's Doxygen.
@@ -53,9 +65,21 @@ class IbexSolver final : public SolverBase {
 
   /// @name Static versions of the instance methods with similar names.
   //@{
+  DRAKE_DEPRECATED("2023-02-01",
+      "IBEX support is being withdrawn from Drake; for details, see "
+      "https://github.com/RobotLocomotion/drake/pull/18156")
   static SolverId id();
+  DRAKE_DEPRECATED("2023-02-01",
+      "IBEX support is being withdrawn from Drake; for details, see "
+      "https://github.com/RobotLocomotion/drake/pull/18156")
   static bool is_available();
+  DRAKE_DEPRECATED("2023-02-01",
+      "IBEX support is being withdrawn from Drake; for details, see "
+      "https://github.com/RobotLocomotion/drake/pull/18156")
   static bool is_enabled();
+  DRAKE_DEPRECATED("2023-02-01",
+      "IBEX support is being withdrawn from Drake; for details, see "
+      "https://github.com/RobotLocomotion/drake/pull/18156")
   static bool ProgramAttributesSatisfied(const MathematicalProgram&);
   //@}
 
diff --git a/solvers/ibex_solver_common.cc b/solvers/ibex_solver_common.cc
index 13dad66d08f6..5135b96364b3 100644
--- a/solvers/ibex_solver_common.cc
+++ b/solvers/ibex_solver_common.cc
@@ -8,6 +8,9 @@
 // This file contains implementations that are common to both the available and
 // unavailable flavor of this class.
 
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
+
 namespace drake {
 namespace solvers {
 
@@ -45,3 +48,5 @@ bool IbexSolver::ProgramAttributesSatisfied(const MathematicalProgram& prog) {
 
 }  // namespace solvers
 }  // namespace drake
+
+#pragma GCC diagnostic pop
diff --git a/solvers/solver_type.h b/solvers/solver_type.h
index 9c0ca86c2444..f89602af415b 100644
--- a/solvers/solver_type.h
+++ b/solvers/solver_type.h
@@ -8,10 +8,8 @@ new code. */
 enum class SolverType {
   kClp,
   kCsdp,
-  kDReal,
   kEqualityConstrainedQP,
   kGurobi,
-  kIbex,
   kIpopt,
   kLinearSystem,
   kMobyLCP,
@@ -21,6 +19,8 @@ enum class SolverType {
   kSnopt,
   kScs,
   kUnrevisedLemke
+  , kDReal [[deprecated("DRAKE DEPRECATED: dReal support is being withdrawn from Drake; for details, see https://github.com/RobotLocomotion/drake/pull/18156. The deprecated code will be removed from Drake on or after 2023-02-01")]]  // NOLINT
+  , kIbex  [[deprecated("DRAKE DEPRECATED: IBEX support is being withdrawn from Drake; for details, see https://github.com/RobotLocomotion/drake/pull/18156. The deprecated code will be removed from Drake on or after 2023-02-01")]]  // NOLINT
 };
 
 }  // namespace solvers
diff --git a/solvers/solver_type_converter.cc b/solvers/solver_type_converter.cc
index 20b54bad0c5f..fd038bfb3dab 100644
--- a/solvers/solver_type_converter.cc
+++ b/solvers/solver_type_converter.cc
@@ -26,14 +26,10 @@ SolverId SolverTypeConverter::TypeToId(SolverType solver_type) {
       return ClpSolver::id();
     case SolverType::kCsdp:
       return CsdpSolver::id();
-    case SolverType::kDReal:
-      return DrealSolver::id();
     case SolverType::kEqualityConstrainedQP:
       return EqualityConstrainedQPSolver::id();
     case SolverType::kGurobi:
       return GurobiSolver::id();
-    case SolverType::kIbex:
-      return IbexSolver::id();
     case SolverType::kIpopt:
       return IpoptSolver::id();
     case SolverType::kLinearSystem:
@@ -52,6 +48,13 @@ SolverId SolverTypeConverter::TypeToId(SolverType solver_type) {
       return ScsSolver::id();
     case SolverType::kUnrevisedLemke:
       return UnrevisedLemkeSolverId::id();
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
+    case SolverType::kDReal:
+      return DrealSolver::id();
+    case SolverType::kIbex:
+      return IbexSolver::id();
+#pragma GCC diagnostic pop
   }
   DRAKE_UNREACHABLE();
 }
@@ -61,14 +64,10 @@ std::optional<SolverType> SolverTypeConverter::IdToType(SolverId solver_id) {
     return SolverType::kClp;
   } else if (solver_id == CsdpSolver::id()) {
     return SolverType::kCsdp;
-  } else if (solver_id == DrealSolver::id()) {
-    return SolverType::kDReal;
   } else if (solver_id == EqualityConstrainedQPSolver::id()) {
     return SolverType::kEqualityConstrainedQP;
   } else if (solver_id == GurobiSolver::id()) {
     return SolverType::kGurobi;
-  } else if (solver_id == IbexSolver::id()) {
-    return SolverType::kIbex;
   } else if (solver_id == IpoptSolver::id()) {
     return SolverType::kIpopt;
   } else if (solver_id == LinearSystemSolver::id()) {
@@ -87,6 +86,13 @@ std::optional<SolverType> SolverTypeConverter::IdToType(SolverId solver_id) {
     return SolverType::kScs;
   } else if (solver_id == UnrevisedLemkeSolverId::id()) {
     return SolverType::kUnrevisedLemke;
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
+  } else if (solver_id == DrealSolver::id()) {
+    return SolverType::kDReal;
+  } else if (solver_id == IbexSolver::id()) {
+    return SolverType::kIbex;
+#pragma GCC diagnostic pop
   } else {
     return std::nullopt;
   }
diff --git a/solvers/test/solver_type_converter_test.cc b/solvers/test/solver_type_converter_test.cc
index c74c2e769705..86b9ccf9c064 100644
--- a/solvers/test/solver_type_converter_test.cc
+++ b/solvers/test/solver_type_converter_test.cc
@@ -18,14 +18,10 @@ std::optional<SolverType> successor(std::optional<SolverType> solver_type) {
     case SolverType::kClp:
       return SolverType::kCsdp;
     case SolverType::kCsdp:
-      return SolverType::kDReal;
-    case SolverType::kDReal:
       return SolverType::kEqualityConstrainedQP;
     case SolverType::kEqualityConstrainedQP:
       return SolverType::kGurobi;
     case SolverType::kGurobi:
-      return SolverType::kIbex;
-    case SolverType::kIbex:
       return SolverType::kIpopt;
     case SolverType::kIpopt:
       return SolverType::kLinearSystem;
@@ -44,6 +40,13 @@ std::optional<SolverType> successor(std::optional<SolverType> solver_type) {
     case SolverType::kSnopt:
       return SolverType::kUnrevisedLemke;
     case SolverType::kUnrevisedLemke:
+#pragma GCC diagnostic push
+#pragma GCC diagnostic ignored "-Wdeprecated-declarations"
+      return SolverType::kDReal;
+    case SolverType::kDReal:
+      return SolverType::kIbex;
+    case SolverType::kIbex:
+#pragma GCC diagnostic pop
       return std::nullopt;
   }
   DRAKE_UNREACHABLE();
diff --git a/tools/workspace/cds/repository.bzl b/tools/workspace/cds/repository.bzl
index 406906da1486..cd6cfaa0c3cd 100644
--- a/tools/workspace/cds/repository.bzl
+++ b/tools/workspace/cds/repository.bzl
@@ -2,6 +2,9 @@
 
 load("@drake//tools/workspace:github.bzl", "github_archive")
 
+# N.B. This repository is deprecated for removal on 2023-02-01.
+# For details see https://github.com/RobotLocomotion/drake/pull/18156.
+
 def cds_repository(
         name,
         mirrors = None):
diff --git a/tools/workspace/default.bzl b/tools/workspace/default.bzl
index f9bfe8e08825..db79bfa95243 100644
--- a/tools/workspace/default.bzl
+++ b/tools/workspace/default.bzl
@@ -127,6 +127,8 @@ def add_default_repositories(excludes = [], mirrors = DEFAULT_MIRRORS):
     if "ccd" not in excludes:
         ccd_repository(name = "ccd", mirrors = mirrors)
     if "cds" not in excludes:
+        # N.B. This repository is deprecated for removal on 2023-02-01.
+        # For details see https://github.com/RobotLocomotion/drake/pull/18156.
         cds_repository(name = "cds", mirrors = mirrors)
     if "clang_cindex_python3_internal" not in excludes:
         clang_cindex_python3_internal_repository(name = "clang_cindex_python3_internal", mirrors = mirrors)  # noqa
@@ -155,6 +157,8 @@ def add_default_repositories(excludes = [], mirrors = DEFAULT_MIRRORS):
     if "drake_visualizer" not in excludes:
         drake_visualizer_repository(name = "drake_visualizer", mirrors = mirrors)  # noqa
     if "dreal" not in excludes:
+        # N.B. This repository is deprecated for removal on 2023-02-01.
+        # For details see https://github.com/RobotLocomotion/drake/pull/18156.
         dreal_repository(name = "dreal", mirrors = mirrors)
     if "eigen" not in excludes:
         eigen_repository(name = "eigen")
@@ -189,6 +193,8 @@ def add_default_repositories(excludes = [], mirrors = DEFAULT_MIRRORS):
     if "gz_utils_internal" not in excludes:
         gz_utils_internal_repository(name = "gz_utils_internal", mirrors = mirrors)  # noqa
     if "ibex" not in excludes:
+        # N.B. This repository is deprecated for removal on 2023-02-01.
+        # For details see https://github.com/RobotLocomotion/drake/pull/18156.
         ibex_repository(name = "ibex", mirrors = mirrors)
     if "intel_realsense_ros_internal" not in excludes:
         intel_realsense_ros_internal_repository(name = "intel_realsense_ros_internal", mirrors = mirrors)  # noqa
@@ -257,6 +263,8 @@ def add_default_repositories(excludes = [], mirrors = DEFAULT_MIRRORS):
     if "petsc" not in excludes:
         petsc_repository(name = "petsc", mirrors = mirrors)
     if "picosat" not in excludes:
+        # N.B. This repository is deprecated for removal on 2023-02-01.
+        # For details see https://github.com/RobotLocomotion/drake/pull/18156.
         picosat_repository(name = "picosat", mirrors = mirrors)
     if "picosha2" not in excludes:
         picosha2_repository(name = "picosha2", mirrors = mirrors)
diff --git a/tools/workspace/dreal/repository.bzl b/tools/workspace/dreal/repository.bzl
index 9467a4d0b043..1889b82a4c52 100644
--- a/tools/workspace/dreal/repository.bzl
+++ b/tools/workspace/dreal/repository.bzl
@@ -2,6 +2,9 @@
 
 load("@drake//tools/workspace:github.bzl", "github_archive")
 
+# N.B. This repository is deprecated for removal on 2023-02-01.
+# For details see https://github.com/RobotLocomotion/drake/pull/18156.
+
 def dreal_repository(
         name,
         mirrors = None):
diff --git a/tools/workspace/ibex/repository.bzl b/tools/workspace/ibex/repository.bzl
index a831266486d9..6dc9649ed616 100644
--- a/tools/workspace/ibex/repository.bzl
+++ b/tools/workspace/ibex/repository.bzl
@@ -2,13 +2,14 @@
 
 load("@drake//tools/workspace:github.bzl", "github_archive")
 
+# N.B. This repository is deprecated for removal on 2023-02-01.
+# For details see https://github.com/RobotLocomotion/drake/pull/18156.
+
 def ibex_repository(
         name,
         mirrors = None):
     github_archive(
         name = name,
-        # TODO(jwnimmer-tri) Switch to upstream ibex-lib (using local patch
-        # files if necessary).
         repository = "dreal-deps/ibex-lib",
         # As discussed in #15872, we need ibex < 2.8.7 for CLP support.
         commit = "115e12323529d524786c1a744f5ffce04f4783b5",  # ibex-2.8.6_4
diff --git a/tools/workspace/picosat/repository.bzl b/tools/workspace/picosat/repository.bzl
index 4e539a1ea8ad..7f5e04f73113 100644
--- a/tools/workspace/picosat/repository.bzl
+++ b/tools/workspace/picosat/repository.bzl
@@ -2,8 +2,8 @@
 
 load("@drake//tools/workspace:github.bzl", "github_archive")
 
-# TODO(jwnimmer-tri) For easier ugprades, stop using the dreal-deps mirror and
-# switch to using the upstream archive at http://fmv.jku.at/picosat/.
+# N.B. This repository is deprecated for removal on 2023-02-01.
+# For details see https://github.com/RobotLocomotion/drake/pull/18156.
 
 def picosat_repository(
         name,