diff --git a/qiskit/circuit/library/n_local/n_local.py b/qiskit/circuit/library/n_local/n_local.py
index b3db02b94f03..1188436a9e8d 100644
--- a/qiskit/circuit/library/n_local/n_local.py
+++ b/qiskit/circuit/library/n_local/n_local.py
@@ -21,7 +21,6 @@
 from qiskit.circuit.quantumregister import QuantumRegister
 from qiskit.circuit import Instruction, Parameter, ParameterVector, ParameterExpression
 from qiskit.circuit.parametertable import ParameterTable
-from qiskit.utils.deprecation import deprecate_arguments
 
 from ..blueprintcircuit import BlueprintCircuit
 
@@ -793,12 +792,10 @@ def add_layer(
 
         return self
 
-    @deprecate_arguments({"param_dict": "parameters"})
     def assign_parameters(
         self,
         parameters: Union[dict, List[float], List[Parameter], ParameterVector],
         inplace: bool = False,
-        param_dict: Optional[dict] = None,
     ) -> Optional[QuantumCircuit]:
         """Assign parameters to the n-local circuit.
 
diff --git a/qiskit/circuit/quantumcircuit.py b/qiskit/circuit/quantumcircuit.py
index 82013a7f3b04..d49371217e4e 100644
--- a/qiskit/circuit/quantumcircuit.py
+++ b/qiskit/circuit/quantumcircuit.py
@@ -31,7 +31,7 @@
 from qiskit.qasm.qasm import Qasm
 from qiskit.qasm.exceptions import QasmError
 from qiskit.circuit.exceptions import CircuitError
-from qiskit.utils.deprecation import deprecate_function, deprecate_arguments
+from qiskit.utils.deprecation import deprecate_function
 from .parameterexpression import ParameterExpression
 from .quantumregister import QuantumRegister, Qubit, AncillaRegister, AncillaQubit
 from .classicalregister import ClassicalRegister, Clbit
@@ -2128,10 +2128,7 @@ def _unsorted_parameters(self):
 
         return parameters
 
-    @deprecate_arguments({"param_dict": "parameters"})
-    def assign_parameters(
-        self, parameters, inplace=False, param_dict=None
-    ):  # pylint: disable=unused-argument
+    def assign_parameters(self, parameters, inplace=False):
         """Assign parameters to new parameters or values.
 
         The keys of the parameter dictionary must be Parameter instances in the current circuit. The
@@ -2143,11 +2140,9 @@ def assign_parameters(
                 parameter values. If a dict, it specifies the mapping from ``current_parameter`` to
                 ``new_parameter``, where ``new_parameter`` can be a new parameter object or a
                 numeric value. If an iterable, the elements are assigned to the existing parameters
-                in the order they were inserted. You can call ``QuantumCircuit.parameters`` to check
-                this order.
+                in the order of ``QuantumCircuit.parameters``.
             inplace (bool): If False, a copy of the circuit with the bound parameters is
                 returned. If True the circuit instance itself is modified.
-            param_dict (dict): Deprecated, use ``parameters`` instead.
 
         Raises:
             CircuitError: If parameters is a dict and contains parameters not present in the
@@ -2238,8 +2233,7 @@ def assign_parameters(
                 bound_circuit._assign_parameter(self.parameters[i], value)
         return None if inplace else bound_circuit
 
-    @deprecate_arguments({"value_dict": "values"})
-    def bind_parameters(self, values, value_dict=None):  # pylint: disable=unused-argument
+    def bind_parameters(self, values):
         """Assign numeric parameters to values yielding a new circuit.
 
         To assign new Parameter objects or bind the values in-place, without yielding a new
@@ -2247,7 +2241,6 @@ def bind_parameters(self, values, value_dict=None):  # pylint: disable=unused-ar
 
         Args:
             values (dict or iterable): {parameter: value, ...} or [value1, value2, ...]
-            value_dict (dict): Deprecated, use ``values`` instead.
 
         Raises:
             CircuitError: If values is a dict and contains parameters not present in the circuit.
diff --git a/releasenotes/notes/remove-deprecated-assign-parameters-args-9712d7d01e82c390.yaml b/releasenotes/notes/remove-deprecated-assign-parameters-args-9712d7d01e82c390.yaml
new file mode 100644
index 000000000000..b18198b897cd
--- /dev/null
+++ b/releasenotes/notes/remove-deprecated-assign-parameters-args-9712d7d01e82c390.yaml
@@ -0,0 +1,14 @@
+---
+upgrade:
+  - |
+    Delete the arguments `param_dict` in :meth:`qiskit.circuit.QuantumCircuit.assign_parameters`
+    and `value_dict` in :meth:`qiskit.circuit.QuantumCircuit.bind_parameters`, which have been
+    deprecated in [PR 5759](https://github.com/Qiskit/qiskit-terra/pull/5759). Instead,
+    use the arguments `parameters` resp. `values`.
+fixes:
+  - |
+    Fix the statement about the parameter order if the parameters are provided as 
+    iteratble and not dictionary in 
+    :meth:`qiskit.circuit.QuantumCircuit.assign_parameters`. The parameters are not 
+    sorted by insertion but by name, with the special case that the order of a 
+    :class:`~qiskit.circuit.ParameterVector` is maintained.