diff --git a/CHANGELOG.md b/CHANGELOG.md
index 5e789f28249e..a348346fae30 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -20,6 +20,8 @@ Remember to align the itemized text with the first line of an item within a list
     deprecated and will soon be removed. Use `rtol` instead.
   * The ``rcond`` argument of {func}`jax.numpy.linalg.pinv` is being
     deprecated and will soon be removed. Use `rtol` instead.
+  * The ``ddof`` argument of {func}`jax.numpy.std` and {func}`jax.numpy.std` is being
+    deprecated and will soon be removed. Use `correction` instead.
 
 ## jaxlib 0.4.29
 
diff --git a/jax/_src/numpy/reductions.py b/jax/_src/numpy/reductions.py
index 0eca75fbbb23..c0bfdf5bd854 100644
--- a/jax/_src/numpy/reductions.py
+++ b/jax/_src/numpy/reductions.py
@@ -434,7 +434,7 @@ def _average(a: ArrayLike, axis: Axis = None, weights: ArrayLike | None = None,
 def var(a: ArrayLike, axis: Axis = None, dtype: DTypeLike | None = None,
         out: None = None, correction: int | float = 0, keepdims: bool = False, *,
         where: ArrayLike | None = None, ddof: int | DeprecatedArg = DeprecatedArg()) -> Array:
-  # TODO(vfdev-5): deprecated 2024-5-16, remove after deprecation expires.
+  # TODO(vfdev-5): Remove after deprecation is completed (began 2024-5-16)
   if not isinstance(ddof, DeprecatedArg):
     warnings.warn(
       "The ddof argument of jax.numpy.var is deprecated and setting it "
@@ -503,10 +503,10 @@ def _var_promote_types(a_dtype: DTypeLike, dtype: DTypeLike | None) -> tuple[DTy
 def std(a: ArrayLike, axis: Axis = None, dtype: DTypeLike | None = None,
         out: None = None, correction: int | float = 0, keepdims: bool = False, *,
         where: ArrayLike | None = None, ddof: int | DeprecatedArg = DeprecatedArg()) -> Array:
-  # TODO(vfdev-5): deprecated 2024-5-16, remove after deprecation expires.
+  # TODO(vfdev-5): Remove after deprecation is completed (began 2024-5-16)
   if not isinstance(ddof, DeprecatedArg):
     warnings.warn(
-      "The ddof argument of jax.numpy.var is deprecated and setting it "
+      "The ddof argument of jax.numpy.std is deprecated and setting it "
       "will soon raise an error. To avoid an error in the future, and to "
       "suppress this warning, please use the correction argument instead.",
       DeprecationWarning, stacklevel=2)
diff --git a/jax/numpy/__init__.pyi b/jax/numpy/__init__.pyi
index 36a6347d35ba..97b7f34e94e9 100644
--- a/jax/numpy/__init__.pyi
+++ b/jax/numpy/__init__.pyi
@@ -782,8 +782,8 @@ def stack(
     dtype: Optional[DTypeLike] = ...,
 ) -> Array: ...
 def std(a: ArrayLike, axis: _Axis = ..., dtype: DTypeLike = ...,
-        out: None = ..., ddof: int = ..., keepdims: builtins.bool = ..., *,
-        where: Optional[ArrayLike] = ...) -> Array: ...
+        out: None = ..., correction: int | float = ..., keepdims: builtins.bool = ..., *,
+        where: Optional[ArrayLike] = ..., ddof: int | DeprecatedArg = ...) -> Array: ...
 def subtract(x: ArrayLike, y: ArrayLike, /) -> Array: ...
 def sum(
     a: ArrayLike,
@@ -893,8 +893,8 @@ def vander(
     x: ArrayLike, N: Optional[int] = ..., increasing: builtins.bool = ...
 ) -> Array: ...
 def var(a: ArrayLike, axis: _Axis = ..., dtype: DTypeLike = ...,
-        out: None = ..., ddof: int = ..., keepdims: builtins.bool = ..., *,
-        where: Optional[ArrayLike] = ...) -> Array: ...
+        out: None = ..., correction: int | float = ..., keepdims: builtins.bool = ..., *,
+        where: Optional[ArrayLike] = ..., ddof: int | DeprecatedArg = ...) -> Array: ...
 def vdot(
     a: ArrayLike, b: ArrayLike, *, precision: PrecisionLike = ...,
     preferred_element_type: Optional[DTypeLike] = ...) -> Array: ...