diff --git a/pytorch_lightning/callbacks/model_checkpoint.py b/pytorch_lightning/callbacks/model_checkpoint.py
index ebf7017e26..43ef28c7d8 100644
--- a/pytorch_lightning/callbacks/model_checkpoint.py
+++ b/pytorch_lightning/callbacks/model_checkpoint.py
@@ -402,6 +402,7 @@ class ModelCheckpoint(Callback):
             self._save_model(filepath, trainer, pl_module)
             if self.last_model_path and self.last_model_path != filepath:
                 self._del_model(self.last_model_path)
+            self.last_model_path = filepath
 
     def _is_valid_monitor_key(self, metrics):
         return self.monitor in metrics or len(metrics) == 0
diff --git a/tests/callbacks/test_model_checkpoint.py b/tests/callbacks/test_model_checkpoint.py
index 39c733922a..f7db35fe04 100644
--- a/tests/callbacks/test_model_checkpoint.py
+++ b/tests/callbacks/test_model_checkpoint.py
@@ -150,12 +150,33 @@ def test_model_checkpoint_format_checkpoint_name(tmpdir):
     assert ckpt_name == tmpdir / 'test-name-v3.ckpt'
 
 
+def test_model_checkpoint_save_last(tmpdir):
+    """Tests that save_last produces only one last checkpoint."""
+    model = EvalModelTemplate()
+    epochs = 3
+    ModelCheckpoint.CHECKPOINT_NAME_LAST = 'last-{epoch}'
+    model_checkpoint = ModelCheckpoint(filepath=tmpdir, save_top_k=-1, save_last=True)
+    trainer = Trainer(
+        default_root_dir=tmpdir,
+        early_stop_callback=False,
+        checkpoint_callback=model_checkpoint,
+        max_epochs=epochs,
+    )
+    trainer.fit(model)
+    last_filename = model_checkpoint._format_checkpoint_name(ModelCheckpoint.CHECKPOINT_NAME_LAST, epochs - 1, {})
+    last_filename = last_filename + '.ckpt'
+    assert str(tmpdir / last_filename) == model_checkpoint.last_model_path
+    assert set(os.listdir(tmpdir)) == set(
+        [f'epoch={i}.ckpt' for i in range(epochs)] + [last_filename, 'lightning_logs']
+    )
+    ModelCheckpoint.CHECKPOINT_NAME_LAST = 'last'
+
+
 def test_model_checkpoint_save_last_checkpoint_contents(tmpdir):
     """Tests that the save_last checkpoint contains the latest information."""
     seed_everything(100)
     model = EvalModelTemplate()
     num_epochs = 3
-    ModelCheckpoint.CHECKPOINT_NAME_LAST = 'last-{epoch}'
     model_checkpoint = ModelCheckpoint(filepath=tmpdir, save_top_k=num_epochs, save_last=True)
     trainer = Trainer(
         default_root_dir=tmpdir,
@@ -164,30 +185,23 @@ def test_model_checkpoint_save_last_checkpoint_contents(tmpdir):
         max_epochs=num_epochs,
     )
     trainer.fit(model)
-    last_filename = model_checkpoint._format_checkpoint_name(ModelCheckpoint.CHECKPOINT_NAME_LAST, num_epochs - 1, {})
-    path_last_epoch = model_checkpoint.format_checkpoint_name(num_epochs - 1, {})  # epoch=3.ckpt
-    path_last = str(tmpdir / f'{last_filename}.ckpt')  # last-epoch=3.ckpt
-    assert path_last_epoch != path_last
+
+    path_last_epoch = model_checkpoint.format_checkpoint_name(num_epochs - 1, {})
+    assert path_last_epoch != model_checkpoint.last_model_path
+
     ckpt_last_epoch = torch.load(path_last_epoch)
-    ckpt_last = torch.load(path_last)
-
-    trainer_keys = ("epoch", "global_step")
-    for key in trainer_keys:
-        assert ckpt_last_epoch[key] == ckpt_last[key]
-
-    checkpoint_callback_keys = ("best_model_score", "best_model_path")
-    for key in checkpoint_callback_keys:
-        assert (
-            ckpt_last["callbacks"][type(model_checkpoint)][key]
-            == ckpt_last_epoch["callbacks"][type(model_checkpoint)][key]
-        )
+    ckpt_last = torch.load(model_checkpoint.last_model_path)
+    assert all(ckpt_last_epoch[k] == ckpt_last[k] for k in ("epoch", "global_step"))
+    assert all(
+        ckpt_last["callbacks"][type(model_checkpoint)][k] == ckpt_last_epoch["callbacks"][type(model_checkpoint)][k]
+        for k in ("best_model_score", "best_model_path")
+    )
 
     # it is easier to load the model objects than to iterate over the raw dict of tensors
     model_last_epoch = EvalModelTemplate.load_from_checkpoint(path_last_epoch)
-    model_last = EvalModelTemplate.load_from_checkpoint(path_last)
+    model_last = EvalModelTemplate.load_from_checkpoint(model_checkpoint.last_model_path)
     for w0, w1 in zip(model_last_epoch.parameters(), model_last.parameters()):
         assert w0.eq(w1).all()
-    ModelCheckpoint.CHECKPOINT_NAME_LAST = 'last'
 
 
 def test_ckpt_metric_names(tmpdir):