diff --git a/sklearn/model_selection/_search.py b/sklearn/model_selection/_search.py
index 864567dabad11..db6e12cc1b9f3 100644
--- a/sklearn/model_selection/_search.py
+++ b/sklearn/model_selection/_search.py
@@ -858,6 +858,9 @@ def evaluate_candidates(candidate_params, cv=None, more_results=None):
             refit_end_time = time.time()
             self.refit_time_ = refit_end_time - refit_start_time
 
+            if hasattr(self.best_estimator_, "feature_names_in_"):
+                self.feature_names_in_ = self.best_estimator_.feature_names_in_
+
         # Store the only scorer not as a dict for single metric evaluation
         self.scorer_ = scorers
 
@@ -1246,11 +1249,21 @@ class GridSearchCV(BaseSearchCV):
         the underlying estimator is a classifier.
 
     n_features_in_ : int
-        Number of features seen during :term:`fit`. Only defined if the
-        underlying estimator exposes such an attribute when fit.
+        Number of features seen during :term:`fit`. Only defined if
+        `best_estimator_` is defined (see the documentation for the `refit`
+        parameter for more details) and that `best_estimator_` exposes
+        `n_features_in_` when fit.
 
         .. versionadded:: 0.24
 
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Only defined if
+        `best_estimator_` is defined (see the documentation for the `refit`
+        parameter for more details) and that `best_estimator_` exposes
+        `feature_names_in_` when fit.
+
+        .. versionadded:: 1.0
+
     Notes
     -----
     The parameters selected are those that maximize the score of the left out
@@ -1595,11 +1608,21 @@ class RandomizedSearchCV(BaseSearchCV):
         the underlying estimator is a classifier.
 
     n_features_in_ : int
-        Number of features seen during :term:`fit`. Only defined if the
-        underlying estimator exposes such an attribute when fit.
+        Number of features seen during :term:`fit`. Only defined if
+        `best_estimator_` is defined (see the documentation for the `refit`
+        parameter for more details) and that `best_estimator_` exposes
+        `n_features_in_` when fit.
 
         .. versionadded:: 0.24
 
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Only defined if
+        `best_estimator_` is defined (see the documentation for the `refit`
+        parameter for more details) and that `best_estimator_` exposes
+        `feature_names_in_` when fit.
+
+        .. versionadded:: 1.0
+
     Notes
     -----
     The parameters selected are those that maximize the score of the held-out
diff --git a/sklearn/model_selection/_search_successive_halving.py b/sklearn/model_selection/_search_successive_halving.py
index ec7692af7f509..a040c0f4e74c3 100644
--- a/sklearn/model_selection/_search_successive_halving.py
+++ b/sklearn/model_selection/_search_successive_halving.py
@@ -626,11 +626,21 @@ class HalvingGridSearchCV(BaseSuccessiveHalving):
         the underlying estimator is a classifier.
 
     n_features_in_ : int
-        Number of features seen during :term:`fit`. Only defined if the
-        underlying estimator exposes such an attribute when fit.
+        Number of features seen during :term:`fit`. Only defined if
+        `best_estimator_` is defined (see the documentation for the `refit`
+        parameter for more details) and that `best_estimator_` exposes
+        `n_features_in_` when fit.
 
         .. versionadded:: 0.24
 
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Only defined if
+        `best_estimator_` is defined (see the documentation for the `refit`
+        parameter for more details) and that `best_estimator_` exposes
+        `feature_names_in_` when fit.
+
+        .. versionadded:: 1.0
+
     See Also
     --------
     :class:`HalvingRandomSearchCV`:
@@ -954,11 +964,21 @@ class HalvingRandomSearchCV(BaseSuccessiveHalving):
         the underlying estimator is a classifier.
 
     n_features_in_ : int
-        Number of features seen during :term:`fit`. Only defined if the
-        underlying estimator exposes such an attribute when fit.
+        Number of features seen during :term:`fit`. Only defined if
+        `best_estimator_` is defined (see the documentation for the `refit`
+        parameter for more details) and that `best_estimator_` exposes
+        `n_features_in_` when fit.
 
         .. versionadded:: 0.24
 
+    feature_names_in_ : ndarray of shape (`n_features_in_`,)
+        Names of features seen during :term:`fit`. Only defined if
+        `best_estimator_` is defined (see the documentation for the `refit`
+        parameter for more details) and that `best_estimator_` exposes
+        `feature_names_in_` when fit.
+
+        .. versionadded:: 1.0
+
     See Also
     --------
     :class:`HalvingGridSearchCV`:
diff --git a/sklearn/tests/test_common.py b/sklearn/tests/test_common.py
index e9090780f9eb1..f245f940cc943 100644
--- a/sklearn/tests/test_common.py
+++ b/sklearn/tests/test_common.py
@@ -325,11 +325,14 @@ def test_check_n_features_in_after_fitting(estimator):
 
 COLUMN_NAME_MODULES_TO_IGNORE = {
     "compose",
-    "model_selection",
 }
 
 _estimators_to_test = list(
-    chain(_tested_estimators(), [make_pipeline(LogisticRegression(C=1))])
+    chain(
+        _tested_estimators(),
+        [make_pipeline(LogisticRegression(C=1))],
+        list(_generate_search_cv_instances()),
+    )
 )