diff --git a/src/pytorch_lightning/CHANGELOG.md b/src/pytorch_lightning/CHANGELOG.md
index 6085c026f9553..c12ea445e1b5a 100644
--- a/src/pytorch_lightning/CHANGELOG.md
+++ b/src/pytorch_lightning/CHANGELOG.md
@@ -224,6 +224,7 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 
 - Removed the deprecated `SimpleProfiler.profile_iterable` and `AdvancedProfiler.profile_iterable` attributes ([#14864](https://github.com/Lightning-AI/lightning/pull/14864))
 
+- Remove the deprecated `Trainer.should_rank_save_checkpoint` ([#14885](https://github.com/Lightning-AI/lightning/pull/14885))
 
 ### Fixed
 
diff --git a/src/pytorch_lightning/trainer/trainer.py b/src/pytorch_lightning/trainer/trainer.py
index c438b2f767d91..6f3e0d4ce7c4c 100644
--- a/src/pytorch_lightning/trainer/trainer.py
+++ b/src/pytorch_lightning/trainer/trainer.py
@@ -1755,16 +1755,6 @@ def world_size(self) -> int:
         # some strategies define a world size
         return getattr(self.strategy, "world_size", 1)
 
-    @property
-    def should_rank_save_checkpoint(self) -> bool:
-        rank_zero_deprecation(
-            "`Trainer.should_rank_save_checkpoint` is deprecated in v1.6 and will be removed in v1.8.", stacklevel=5
-        )
-        strategy = self.strategy
-        return (
-            isinstance(strategy, pl.strategies.TPUSpawnStrategy) and strategy.local_rank == 0 or strategy.is_global_zero
-        )
-
     @property
     def num_nodes(self) -> int:
         return getattr(self.strategy, "num_nodes", 1)
diff --git a/tests/tests_pytorch/deprecated_api/test_remove_1-8.py b/tests/tests_pytorch/deprecated_api/test_remove_1-8.py
index a7ba047b05c7f..aa25c1cdda8ed 100644
--- a/tests/tests_pytorch/deprecated_api/test_remove_1-8.py
+++ b/tests/tests_pytorch/deprecated_api/test_remove_1-8.py
@@ -91,14 +91,6 @@ def test_v1_8_0_trainer_ckpt_path_attributes(fn_prefix: str):
         setattr(trainer, test_attr, "v")
 
 
-def test_v1_8_0_deprecated_trainer_should_rank_save_checkpoint(tmpdir):
-    trainer = Trainer()
-    with pytest.deprecated_call(
-        match=r"`Trainer.should_rank_save_checkpoint` is deprecated in v1.6 and will be removed in v1.8."
-    ):
-        _ = trainer.should_rank_save_checkpoint
-
-
 def test_v1_8_0_trainer_optimizers_mixin():
     trainer = Trainer()
     model = BoringModel()