diff --git a/jax/_src/api.py b/jax/_src/api.py
index 597d0c057844..b3cd8b88b3da 100644
--- a/jax/_src/api.py
+++ b/jax/_src/api.py
@@ -24,16 +24,15 @@
 
 import collections
 from collections.abc import Generator, Hashable, Iterable, Sequence
+from contextlib import contextmanager, ExitStack
 from functools import partial
 import inspect
 import math
-import typing
-from typing import (Any, Callable, Literal, NamedTuple, TypeVar, overload,
-                    cast)
+from typing import Any, Callable, Literal, NamedTuple, TypeVar, cast, overload
 import weakref
 
 import numpy as np
-from contextlib import contextmanager, ExitStack
+from typing_extensions import ParamSpec
 
 from jax._src import linear_util as lu
 from jax._src import stages
@@ -96,6 +95,9 @@
 F = TypeVar("F", bound=Callable)
 T = TypeVar("T")
 U = TypeVar("U")
+V_co = TypeVar("V_co", covariant=True)
+P = ParamSpec("P")
+
 
 map, unsafe_map = safe_map, map
 zip, unsafe_zip = safe_zip, zip
@@ -140,7 +142,7 @@ def _update_debug_special_thread_local(_):
 
 
 def jit(
-  fun: Callable,
+  fun: Callable[P, V_co],
   in_shardings=sharding_impls.UNSPECIFIED,
   out_shardings=sharding_impls.UNSPECIFIED,
   static_argnums: int | Sequence[int] | None = None,
@@ -152,7 +154,7 @@ def jit(
   backend: str | None = None,
   inline: bool = False,
   abstracted_axes: Any | None = None,
-) -> pjit.JitWrapped:
+) -> pjit.JitWrapped[P, V_co]:
   """Sets up ``fun`` for just-in-time compilation with XLA.
 
   Args:
@@ -1820,7 +1822,7 @@ def cache_miss(*args, **kwargs):
     ### Decide whether we can support the C++ fast path
     use_fastpath = False
     if execute is not None and isinstance(execute, pxla.ExecuteReplicated):
-      execute_replicated = typing.cast(pxla.ExecuteReplicated, execute)
+      execute_replicated = cast(pxla.ExecuteReplicated, execute)
       use_fastpath = (
         # TODO(sharadmv): Enable effects in replicated computation
         not execute_replicated.has_unordered_effects
@@ -1830,7 +1832,7 @@ def cache_miss(*args, **kwargs):
 
     ### If we can use the fastpath, we return required info to the caller.
     if use_fastpath:
-      execute_replicated = typing.cast(pxla.ExecuteReplicated, execute)
+      execute_replicated = cast(pxla.ExecuteReplicated, execute)
       out_handler = execute_replicated.out_handler
       in_handler = execute_replicated.in_handler
 
diff --git a/jax/_src/stages.py b/jax/_src/stages.py
index 2e36e92276fa..88a75e334737 100644
--- a/jax/_src/stages.py
+++ b/jax/_src/stages.py
@@ -32,9 +32,11 @@
 
 from collections.abc import Sequence
 from dataclasses import dataclass
-from typing import Any, NamedTuple, Protocol, Union
+from typing import Any, Generic, NamedTuple, Protocol, TypeVar, Union
 import warnings
 
+from typing_extensions import ParamSpec
+
 import jax
 
 from jax._src import core
@@ -707,7 +709,11 @@ def cost_analysis(self) -> Any | None:
       return None
 
 
-class Wrapped(Protocol):
+V_co = TypeVar("V_co", covariant=True)
+P = ParamSpec("P")
+
+
+class Wrapped(Protocol, Generic[P, V_co]):
   """A function ready to be specialized, lowered, and compiled.
 
   This protocol reflects the output of functions such as
@@ -716,7 +722,7 @@ class Wrapped(Protocol):
   to compilation, and the result compiled prior to execution.
   """
 
-  def __call__(self, *args, **kwargs):
+  def __call__(self, *args: P.args, **kwargs: P.kwargs) -> V_co:
     """Executes the wrapped function, lowering and compiling as needed."""
     raise NotImplementedError
 
diff --git a/setup.py b/setup.py
index 1c35aa0d859c..3ff3927a5ba2 100644
--- a/setup.py
+++ b/setup.py
@@ -84,6 +84,7 @@ def generate_proto(source):
         # Python versions < 3.10. Can be dropped when 3.10 is the minimum
         # required Python version.
         'importlib_metadata>=4.6;python_version<"3.10"',
+        'typing_extensions>=4.5.0',
     ],
     extras_require={
         # Minimum jaxlib version; used in testing.