diff --git a/doc/api/next_api_changes/deprecations.rst b/doc/api/next_api_changes/deprecations.rst
index 60c0682affc1..23fe738b61c3 100644
--- a/doc/api/next_api_changes/deprecations.rst
+++ b/doc/api/next_api_changes/deprecations.rst
@@ -119,3 +119,8 @@ The following parameters do not have any effect and are deprecated:
 - parameter *quantize* of `.Path.cleaned()`
 - parameter *s* of `.AnnotationBbox.get_fontsize()`
 - parameter *label* of `.Tick`
+
+``Axes.update_datalim_bounds``
+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+This method is deprecated.  Use
+``ax.dataLim.set(Bbox.union([ax.dataLim, bounds]))`` instead.
diff --git a/lib/matplotlib/axes/_base.py b/lib/matplotlib/axes/_base.py
index 5f98cbe2a116..192121134058 100644
--- a/lib/matplotlib/axes/_base.py
+++ b/lib/matplotlib/axes/_base.py
@@ -2099,6 +2099,8 @@ def update_datalim(self, xys, updatex=True, updatey=True):
                                          updatex=updatex, updatey=updatey)
         self.ignore_existing_data_limits = False
 
+    @cbook.deprecated(
+        "3.3", alternative="ax.dataLim.set(Bbox.union([ax.dataLim, bounds]))")
     def update_datalim_bounds(self, bounds):
         """
         Extend the `~.Axes.datalim` Bbox to include the given