diff --git a/pyproject.toml b/pyproject.toml
index c0ca3aa418..163755a742 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -35,7 +35,8 @@ classifiers = [
 ]
 dependencies = [
     "click >= 8.0.0",
-    "typing-extensions >= 3.7.4.3",
+    "typing-extensions >= 3.7.4.3; python_version < '3.8'",
+    "typing-extensions >= 4.13.0; python_version >= '3.8'",
 ]
 readme = "README.md"
 [project.urls]
diff --git a/tests/test_annotated.py b/tests/test_annotated.py
index 09072b3ae1..04fe00a01a 100644
--- a/tests/test_annotated.py
+++ b/tests/test_annotated.py
@@ -2,7 +2,7 @@
 from typer.testing import CliRunner
 from typing_extensions import Annotated
 
-from .utils import needs_py310
+from .utils import needs_py38
 
 runner = CliRunner()
 
@@ -23,7 +23,7 @@ def cmd(val: Annotated[int, typer.Argument()] = 0):
     assert "hello 42" in result.output
 
 
-@needs_py310
+@needs_py38
 def test_annotated_argument_in_string_type_with_default():
     app = typer.Typer()
 
diff --git a/tests/utils.py b/tests/utils.py
index 019b006fa0..4de8771154 100644
--- a/tests/utils.py
+++ b/tests/utils.py
@@ -15,6 +15,8 @@
     shell = None
 
 
+needs_py38 = pytest.mark.skipif(sys.version_info < (3, 8), reason="requires python3.8+")
+
 needs_py310 = pytest.mark.skipif(
     sys.version_info < (3, 10), reason="requires python3.10+"
 )
diff --git a/typer/_inspect.py b/typer/_inspect.py
new file mode 100644
index 0000000000..8fb11d1596
--- /dev/null
+++ b/typer/_inspect.py
@@ -0,0 +1,42 @@
+import inspect
+import sys
+
+if sys.version_info >= (3, 10):
+    from inspect import signature
+elif sys.version_info >= (3, 8):
+    from typing import Any, Callable
+
+    from typing_extensions import get_annotations
+
+    def signature(
+        func: Callable[..., Any], eval_str: bool = False, **kwargs: Any
+    ) -> inspect.Signature:
+        sig = inspect.signature(func, **kwargs)
+        ann = get_annotations(
+            func,
+            globals=kwargs.get("globals"),
+            locals=kwargs.get("locals"),
+            eval_str=eval_str,
+        )
+        return sig.replace(
+            parameters=[
+                param.replace(annotation=ann.get(name, param.annotation))
+                for name, param in sig.parameters.items()
+            ],
+            return_annotation=ann.get("return", sig.return_annotation),
+        )
+else:
+    # Fallback for Python <3.8 to make `inspect.signature` accept the `eval_str`
+    # keyword argument as a no-op. We can't backport support for evaluating
+    # string annotations because only typing-extensions v4.13.0+ provides a
+    # backport of `inspect.get_annotations`, which requires Python 3.8+.
+
+    from typing import Any, Callable
+
+    def signature(
+        func: Callable[..., Any], eval_str: bool = False, **kwargs: Any
+    ) -> inspect.Signature:
+        return inspect.signature(func, **kwargs)
+
+
+__all__ = ["signature"]
diff --git a/typer/utils.py b/typer/utils.py
index 81dc4dd61d..d969469d86 100644
--- a/typer/utils.py
+++ b/typer/utils.py
@@ -1,8 +1,7 @@
-import inspect
-import sys
 from copy import copy
 from typing import Any, Callable, Dict, List, Tuple, Type, cast
 
+from ._inspect import signature as inspect_signature
 from ._typing import Annotated, get_args, get_origin, get_type_hints
 from .models import ArgumentInfo, OptionInfo, ParameterInfo, ParamMeta
 
@@ -105,11 +104,7 @@ def _split_annotation_from_typer_annotations(
 
 
 def get_params_from_function(func: Callable[..., Any]) -> Dict[str, ParamMeta]:
-    if sys.version_info >= (3, 10):
-        signature = inspect.signature(func, eval_str=True)
-    else:
-        signature = inspect.signature(func)
-
+    signature = inspect_signature(func, eval_str=True)
     type_hints = get_type_hints(func)
     params = {}
     for param in signature.parameters.values():