diff --git a/doc/whats_new/v1.2.rst b/doc/whats_new/v1.2.rst
index 0e62b87a2ab48..9536c475bc608 100644
--- a/doc/whats_new/v1.2.rst
+++ b/doc/whats_new/v1.2.rst
@@ -27,6 +27,13 @@ Changes impacting all modules
 Changelog
 ---------
 
+:mod:`sklearn.calibration`
+..........................
+
+- |Fix| A deprecation warning is raised when using the `base_estimator__` prefix
+  to set parameters of the estimator used in :class:`calibration.CalibratedClassifierCV`.
+  :pr:`25477` by :user:`Tim Head <betatim>`.
+
 :mod:`sklearn.cluster`
 ......................
 
@@ -41,6 +48,15 @@ Changelog
   empty selection of columns when `set_output(transform="pandas")`.
   :pr:`25570` by `Thomas Fan`_.
 
+:mod:`sklearn.ensemble`
+.......................
+
+- |Fix| A deprecation warning is raised when using the `base_estimator__` prefix
+  to set parameters of the estimator used in :class:`ensemble.AdaBoostClassifier`,
+  :class:`ensemble.AdaBoostRegressor`, :class:`ensemble.BaggingClassifier`,
+  and :class:`ensemble.BaggingRegressor`.
+  :pr:`25477` by :user:`Tim Head <betatim>`.
+
 :mod:`sklearn.isotonic`
 .......................
 
diff --git a/sklearn/base.py b/sklearn/base.py
index 37c61e4cb34d6..5c7168adabc5e 100644
--- a/sklearn/base.py
+++ b/sklearn/base.py
@@ -227,6 +227,25 @@ def set_params(self, **params):
                 valid_params[key] = value
 
         for key, sub_params in nested_params.items():
+            # TODO(1.4): remove specific handling of "base_estimator".
+            # The "base_estimator" key is special. It was deprecated and
+            # renamed to "estimator" for several estimators. This means we
+            # need to translate it here and set sub-parameters on "estimator",
+            # but only if the user did not explicitly set a value for
+            # "base_estimator".
+            if (
+                key == "base_estimator"
+                and valid_params[key] == "deprecated"
+                and self.__module__.startswith("sklearn.")
+            ):
+                warnings.warn(
+                    f"Parameter 'base_estimator' of {self.__class__.__name__} is"
+                    " deprecated in favor of 'estimator'. See"
+                    f" {self.__class__.__name__}'s docstring for more details.",
+                    FutureWarning,
+                    stacklevel=2,
+                )
+                key = "estimator"
             valid_params[key].set_params(**sub_params)
 
         return self
diff --git a/sklearn/ensemble/tests/test_weight_boosting.py b/sklearn/ensemble/tests/test_weight_boosting.py
index c46b140503fd8..eeaffab09a6c8 100755
--- a/sklearn/ensemble/tests/test_weight_boosting.py
+++ b/sklearn/ensemble/tests/test_weight_boosting.py
@@ -630,3 +630,21 @@ def test_base_estimator_property_deprecated(AdaBoost):
     )
     with pytest.warns(FutureWarning, match=warn_msg):
         model.base_estimator_
+
+
+# TODO(1.4): remove in 1.4
+def test_deprecated_base_estimator_parameters_can_be_set():
+    """Check that setting base_estimator parameters works.
+
+    During the deprecation cycle setting "base_estimator__*" params should
+    work.
+
+    Non-regression test for https://github.com/scikit-learn/scikit-learn/issues/25470
+    """
+    # This implicitly sets "estimator", it is how old code (pre v1.2) would
+    # have instantiated AdaBoostClassifier and back then it would set
+    # "base_estimator".
+    clf = AdaBoostClassifier(DecisionTreeClassifier())
+
+    with pytest.warns(FutureWarning, match="Parameter 'base_estimator' of"):
+        clf.set_params(base_estimator__max_depth=2)