diff --git a/doc/developers/develop.rst b/doc/developers/develop.rst
index 05f6ea26ac80e..ef55be3cdffca 100644
--- a/doc/developers/develop.rst
+++ b/doc/developers/develop.rst
@@ -659,6 +659,9 @@ setting `auto_wrap_output_keys=None` when defining a custom subclass::
         def get_feature_names_out(self, input_features=None):
             ...
 
+The default value for `auto_wrap_output_keys` is `("transform",)`, which automatically
+wraps `fit_transform` and `transform`.
+
 For transformers that return multiple arrays in `transform`, auto wrapping will
 only wrap the first array and not alter the other arrays.
 
diff --git a/sklearn/_config.py b/sklearn/_config.py
index ea5c47499b5b4..e4c398c9c5444 100644
--- a/sklearn/_config.py
+++ b/sklearn/_config.py
@@ -123,7 +123,14 @@ def set_config(
         .. versionadded:: 1.2
 
     transform_output : str, default=None
-        Configure the output container for transform.
+        Configure output of `transform` and `fit_transform`.
+
+        See :ref:`sphx_glr_auto_examples_miscellaneous_plot_set_output.py`
+        for an example on how to use the API.
+
+        - `"default"`: Default output format of a transformer
+        - `"pandas"`: DataFrame output
+        - `None`: Transform configuration is unchanged
 
         .. versionadded:: 1.2
 
@@ -231,7 +238,14 @@ def config_context(
         .. versionadded:: 1.2
 
     transform_output : str, default=None
-        Configure the output container for transform.
+        Configure output of `transform` and `fit_transform`.
+
+        See :ref:`sphx_glr_auto_examples_miscellaneous_plot_set_output.py`
+        for an example on how to use the API.
+
+        - `"default"`: Default output format of a transformer
+        - `"pandas"`: DataFrame output
+        - `None`: Transform configuration is unchanged
 
         .. versionadded:: 1.2
 
diff --git a/sklearn/base.py b/sklearn/base.py
index 3ef2a908cdadf..d7d5d8f6644b5 100644
--- a/sklearn/base.py
+++ b/sklearn/base.py
@@ -808,9 +808,9 @@ def get_submatrix(self, i, data):
 class TransformerMixin(_SetOutputMixin):
     """Mixin class for all transformers in scikit-learn.
 
-    If :term:`get_feature_names_out` is defined and `auto_wrap_output` is True,
-    then `BaseEstimator` will automatically wrap `transform` and `fit_transform` to
-    follow the `set_output` API. See the :ref:`developer_api_set_output` for details.
+    If :term:`get_feature_names_out` is defined, then `BaseEstimator` will
+    automatically wrap `transform` and `fit_transform` to follow the `set_output`
+    API. See the :ref:`developer_api_set_output` for details.
     """
 
     def fit_transform(self, X, y=None, **fit_params):
diff --git a/sklearn/compose/_column_transformer.py b/sklearn/compose/_column_transformer.py
index db7a7016c83ab..1fb81e69647c7 100644
--- a/sklearn/compose/_column_transformer.py
+++ b/sklearn/compose/_column_transformer.py
@@ -265,6 +265,10 @@ def set_output(self, transform=None):
         transform : {"default", "pandas"}, default=None
             Configure output of `transform` and `fit_transform`.
 
+            - `"default"`: Default output format of a transformer
+            - `"pandas"`: DataFrame output
+            - `None`: Transform configuration is unchanged
+
         Returns
         -------
         self : estimator instance
diff --git a/sklearn/pipeline.py b/sklearn/pipeline.py
index 3f74acda1fc29..dff4d4c1cd147 100644
--- a/sklearn/pipeline.py
+++ b/sklearn/pipeline.py
@@ -158,6 +158,10 @@ def set_output(self, transform=None):
         transform : {"default", "pandas"}, default=None
             Configure output of `transform` and `fit_transform`.
 
+            - `"default"`: Default output format of a transformer
+            - `"pandas"`: DataFrame output
+            - `None`: Transform configuration is unchanged
+
         Returns
         -------
         self : estimator instance
@@ -999,6 +1003,10 @@ def set_output(self, transform=None):
         transform : {"default", "pandas"}, default=None
             Configure output of `transform` and `fit_transform`.
 
+            - `"default"`: Default output format of a transformer
+            - `"pandas"`: DataFrame output
+            - `None`: Transform configuration is unchanged
+
         Returns
         -------
         self : estimator instance
diff --git a/sklearn/preprocessing/_function_transformer.py b/sklearn/preprocessing/_function_transformer.py
index 228304bb70091..d4c2cf6de7af2 100644
--- a/sklearn/preprocessing/_function_transformer.py
+++ b/sklearn/preprocessing/_function_transformer.py
@@ -316,12 +316,11 @@ def set_output(self, *, transform=None):
         Parameters
         ----------
         transform : {"default", "pandas"}, default=None
-            Configure output of the following estimator's methods:
+            Configure output of `transform` and `fit_transform`.
 
-            - `"transform"`
-            - `"fit_transform"`
-
-            If `None`, this operation is a no-op.
+            - `"default"`: Default output format of a transformer
+            - `"pandas"`: DataFrame output
+            - `None`: Transform configuration is unchanged
 
         Returns
         -------
diff --git a/sklearn/utils/_set_output.py b/sklearn/utils/_set_output.py
index 525c6e0fe0118..5de296dc62d9b 100644
--- a/sklearn/utils/_set_output.py
+++ b/sklearn/utils/_set_output.py
@@ -167,7 +167,7 @@ class _SetOutputMixin:
     it based on `set_output` of the global configuration.
 
     `set_output` is only defined if `get_feature_names_out` is defined and
-    `auto_wrap_output` is True.
+    `auto_wrap_output_keys` is the default value.
     """
 
     def __init_subclass__(cls, auto_wrap_output_keys=("transform",), **kwargs):
@@ -206,12 +206,11 @@ def set_output(self, *, transform=None):
         Parameters
         ----------
         transform : {"default", "pandas"}, default=None
-            Configure output of the following estimator's methods:
+            Configure output of `transform` and `fit_transform`.
 
-            - `"transform"`
-            - `"fit_transform"`
-
-            If `None`, this operation is a no-op.
+            - `"default"`: Default output format of a transformer
+            - `"pandas"`: DataFrame output
+            - `None`: Transform configuration is unchanged
 
         Returns
         -------