diff --git a/stdlib/functools.pyi b/stdlib/functools.pyi
index 1214e349f605..d5f483d5f81b 100644
--- a/stdlib/functools.pyi
+++ b/stdlib/functools.pyi
@@ -1,9 +1,9 @@
 import sys
 import types
-from _typeshed import IdentityFunction, SupportsAllComparisons, SupportsItems
+from _typeshed import SupportsAllComparisons, SupportsItems
 from collections.abc import Callable, Hashable, Iterable, Sequence, Sized
 from typing import Any, Generic, NamedTuple, TypeVar, overload
-from typing_extensions import Literal, Self, TypeAlias, final
+from typing_extensions import Literal, ParamSpec, Self, TypeAlias, final
 
 if sys.version_info >= (3, 9):
     from types import GenericAlias
@@ -28,10 +28,12 @@ if sys.version_info >= (3, 8):
 if sys.version_info >= (3, 9):
     __all__ += ["cache"]
 
-_AnyCallable: TypeAlias = Callable[..., object]
-
 _T = TypeVar("_T")
 _S = TypeVar("_S")
+_PWrapped = ParamSpec("_PWrapped")
+_RWrapped = TypeVar("_RWrapped")
+_PWrapper = ParamSpec("_PWrapper")
+_RWapper = TypeVar("_RWapper")
 
 @overload
 def reduce(function: Callable[[_T, _S], _T], sequence: Iterable[_S], initial: _T) -> _T: ...
@@ -67,8 +69,22 @@ WRAPPER_ASSIGNMENTS: tuple[
 ]
 WRAPPER_UPDATES: tuple[Literal["__dict__"]]
 
-def update_wrapper(wrapper: _T, wrapped: _AnyCallable, assigned: Sequence[str] = ..., updated: Sequence[str] = ...) -> _T: ...
-def wraps(wrapped: _AnyCallable, assigned: Sequence[str] = ..., updated: Sequence[str] = ...) -> IdentityFunction: ...
+class _Wrapped(Generic[_PWrapped, _RWrapped, _PWrapper, _RWapper]):
+    __wrapped__: Callable[_PWrapped, _RWrapped]
+    def __call__(self, *args: _PWrapper.args, **kwargs: _PWrapper.kwargs) -> _RWapper: ...
+
+class _Wrapper(Generic[_PWrapped, _RWrapped]):
+    def __call__(self, f: Callable[_PWrapper, _RWapper]) -> _Wrapped[_PWrapped, _RWrapped, _PWrapper, _RWapper]: ...
+
+def update_wrapper(
+    wrapper: Callable[_PWrapper, _RWapper],
+    wrapped: Callable[_PWrapped, _RWrapped],
+    assigned: Sequence[str] = ...,
+    updated: Sequence[str] = ...,
+) -> _Wrapped[_PWrapped, _RWrapped, _PWrapper, _RWapper]: ...
+def wraps(
+    wrapped: Callable[_PWrapped, _RWrapped], assigned: Sequence[str] = ..., updated: Sequence[str] = ...
+) -> _Wrapper[_PWrapped, _RWrapped]: ...
 def total_ordering(cls: type[_T]) -> type[_T]: ...
 def cmp_to_key(mycmp: Callable[[_T, _T], int]) -> Callable[[_T], SupportsAllComparisons]: ...