diff --git a/doc/api/next_api_changes/deprecations.rst b/doc/api/next_api_changes/deprecations.rst
index 7e9e32c39444..cd4714c84482 100644
--- a/doc/api/next_api_changes/deprecations.rst
+++ b/doc/api/next_api_changes/deprecations.rst
@@ -199,3 +199,8 @@ The change from "nonpos" to "nonpositive" also affects `~.scale.LogTransform`,
 
 To use *different* bases for the x-axis and y-axis of a `~.Axes.loglog` plot,
 use e.g. ``ax.set_xscale("log", base=10); ax.set_yscale("log", base=2)``.
+
+``DraggableBase.artist_picker``
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+This method is deprecated.  If you previously reimplemented it in a subclass,
+set the artist's picker instead with `.Artist.set_picker`.
diff --git a/lib/matplotlib/offsetbox.py b/lib/matplotlib/offsetbox.py
index 5639455a9839..9a1f800d68d5 100644
--- a/lib/matplotlib/offsetbox.py
+++ b/lib/matplotlib/offsetbox.py
@@ -1694,11 +1694,7 @@ def update_offset(self, dx, dy):
             the point where the mouse drag started.
             '''
 
-    Optionally, you may override the following methods::
-
-        def artist_picker(self, artist, evt):
-            '''The picker method that will be used.'''
-            return self.ref_artist.contains(evt)
+    Optionally, you may override the following method::
 
         def finalize_offset(self):
             '''Called when the mouse is released.'''
@@ -1719,7 +1715,18 @@ def __init__(self, ref_artist, use_blit=False):
         c2 = self.canvas.mpl_connect('pick_event', self.on_pick)
         c3 = self.canvas.mpl_connect('button_release_event', self.on_release)
 
-        ref_artist.set_picker(self.artist_picker)
+        if not ref_artist.pickable():
+            ref_artist.set_picker(True)
+        with cbook._suppress_matplotlib_deprecation_warning():
+            if self.artist_picker != DraggableBase.artist_picker.__get__(self):
+                overridden_picker = self.artist_picker
+            else:
+                overridden_picker = None
+        if overridden_picker is not None:
+            cbook.warn_deprecated(
+                "3.3", name="artist_picker", obj_type="method",
+                addendum="Directly set the artist's picker if desired.")
+            ref_artist.set_picker(overridden_picker)
         self.cids = [c2, c3]
 
     def on_motion(self, evt):
@@ -1786,6 +1793,7 @@ def disconnect(self):
         else:
             self.canvas.mpl_disconnect(c1)
 
+    @cbook.deprecated("3.3", alternative="self.ref_artist.contains")
     def artist_picker(self, artist, evt):
         return self.ref_artist.contains(evt)