diff --git a/lib/matplotlib/axis.py b/lib/matplotlib/axis.py
index 1295d351d0b8..d56af88b64f6 100644
--- a/lib/matplotlib/axis.py
+++ b/lib/matplotlib/axis.py
@@ -2047,19 +2047,15 @@ def _update_offset_text_position(self, bboxes, bboxes2):
             else:
                 bbox = mtransforms.Bbox.union(bboxes)
                 bottom = bbox.y0
-            self.offsetText.set_position(
-                (x, bottom - self.OFFSETTEXTPAD * self.figure.dpi / 72)
-            )
+            y = bottom - self.OFFSETTEXTPAD * self.figure.dpi / 72
         else:
             if not len(bboxes2):
                 top = self.axes.bbox.ymax
             else:
                 bbox = mtransforms.Bbox.union(bboxes2)
                 top = bbox.y1
-            self.offsetText.set_va('top')
-            self.offsetText.set_position(
-                (x, top + self.OFFSETTEXTPAD * self.figure.dpi / 72)
-            )
+            y = top + self.OFFSETTEXTPAD * self.figure.dpi / 72
+        self.offsetText.set_position((x, y))
 
     def get_text_heights(self, renderer):
         """
@@ -2102,10 +2098,12 @@ def set_ticks_position(self, position):
             self.set_tick_params(which='both', top=True, labeltop=True,
                                  bottom=False, labelbottom=False)
             self._tick_position = 'top'
+            self.offsetText.set_verticalalignment('bottom')
         elif position == 'bottom':
             self.set_tick_params(which='both', top=False, labeltop=False,
                                  bottom=True, labelbottom=True)
             self._tick_position = 'bottom'
+            self.offsetText.set_verticalalignment('top')
         elif position == 'both':
             self.set_tick_params(which='both', top=True,
                                  bottom=True)
@@ -2116,6 +2114,7 @@ def set_ticks_position(self, position):
             self.set_tick_params(which='both', top=True, labeltop=False,
                                  bottom=True, labelbottom=True)
             self._tick_position = 'bottom'
+            self.offsetText.set_verticalalignment('top')
         else:
             assert False, "unhandled parameter not caught by _check_in_list"
         self.stale = True
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index 9e12dd95b385..986caba0dd01 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -4641,19 +4641,23 @@ def test_move_offsetlabel():
     ax.plot(data)
     fig.canvas.draw()
     before = ax.yaxis.offsetText.get_position()
+    assert ax.yaxis.offsetText.get_horizontalalignment() == 'left'
     ax.yaxis.tick_right()
     fig.canvas.draw()
     after = ax.yaxis.offsetText.get_position()
     assert after[0] > before[0] and after[1] == before[1]
+    assert ax.yaxis.offsetText.get_horizontalalignment() == 'right'
 
     fig, ax = plt.subplots()
     ax.plot(data)
     fig.canvas.draw()
     before = ax.xaxis.offsetText.get_position()
+    assert ax.xaxis.offsetText.get_verticalalignment() == 'top'
     ax.xaxis.tick_top()
     fig.canvas.draw()
     after = ax.xaxis.offsetText.get_position()
     assert after[0] == before[0] and after[1] > before[1]
+    assert ax.xaxis.offsetText.get_verticalalignment() == 'bottom'
 
 
 @image_comparison(['rc_spines.png'], savefig_kwarg={'dpi': 40})