diff --git a/lib/matplotlib/figure.py b/lib/matplotlib/figure.py
@@ -2533,6 +2533,8 @@ def set_tight_layout(self, tight):
         _tight_parameters = tight if isinstance(tight, dict) else {}
         if bool(tight):
             self.set_layout_engine(TightLayoutEngine(**_tight_parameters))
+        else:
+            self.set_layout_engine(None)
         self.stale = True
 
     def get_constrained_layout(self):
@@ -2569,6 +2571,8 @@ def set_constrained_layout(self, constrained):
         _parameters = constrained if isinstance(constrained, dict) else {}
         if _constrained:
             self.set_layout_engine(ConstrainedLayoutEngine(**_parameters))
+        else:
+            self.set_layout_engine(None)
         self.stale = True
 
     @_api.deprecated(

diff --git a/lib/matplotlib/tests/test_constrainedlayout.py b/lib/matplotlib/tests/test_constrainedlayout.py
@@ -608,3 +608,12 @@ def test_discouraged_api():
 def test_kwargs():
     fig, ax = plt.subplots(constrained_layout={'h_pad': 0.02})
     fig.draw_without_rendering()
+
+
+def test_constrained_toggle():
+    fig, ax = plt.subplots()
+    with pytest.warns(PendingDeprecationWarning):
+        fig.set_constrained_layout(True)
+        assert fig.get_constrained_layout()
+        fig.set_constrained_layout(False)
+        assert not fig.get_constrained_layout()
diff --git a/lib/matplotlib/tests/test_tightlayout.py b/lib/matplotlib/tests/test_tightlayout.py
@@ -380,3 +380,12 @@ def test_tight_pads():
 def test_tight_kwargs():
     fig, ax = plt.subplots(tight_layout={'pad': 0.15})
     fig.draw_without_rendering()
+
+
+def test_tight_toggle():
+    fig, ax = plt.subplots()
+    with pytest.warns(PendingDeprecationWarning):
+        fig.set_tight_layout(True)
+        assert fig.get_tight_layout()
+        fig.set_tight_layout(False)
+        assert not fig.get_tight_layout()