diff --git a/airflow/providers/databricks/operators/databricks.py b/airflow/providers/databricks/operators/databricks.py
index f0ea5b3d0daa2..1f16e5667b9a5 100644
--- a/airflow/providers/databricks/operators/databricks.py
+++ b/airflow/providers/databricks/operators/databricks.py
@@ -921,6 +921,7 @@ class DatabricksNotebookOperator(BaseOperator):
     :param databricks_retry_limit: Amount of times to retry if the Databricks backend is unreachable.
     :param databricks_retry_delay: Number of seconds to wait between retries.
     :param databricks_retry_args: An optional dictionary with arguments passed to ``tenacity.Retrying`` class.
+    :param wait_for_termination: if we should wait for termination of the job run. ``True`` by default.
     :param databricks_conn_id: The name of the Airflow connection to use.
     """
 
@@ -939,6 +940,7 @@ def __init__(
         databricks_retry_limit: int = 3,
         databricks_retry_delay: int = 1,
         databricks_retry_args: dict[Any, Any] | None = None,
+        wait_for_termination: bool = True,
         databricks_conn_id: str = "databricks_default",
         **kwargs: Any,
     ):
@@ -953,8 +955,9 @@ def __init__(
         self.databricks_retry_limit = databricks_retry_limit
         self.databricks_retry_delay = databricks_retry_delay
         self.databricks_retry_args = databricks_retry_args
+        self.wait_for_termination = wait_for_termination
         self.databricks_conn_id = databricks_conn_id
-        self.databricks_run_id = ""
+        self.databricks_run_id: int | None = None
         super().__init__(**kwargs)
 
     @cached_property
@@ -1025,7 +1028,7 @@ def _get_run_json(self) -> dict[str, Any]:
             raise ValueError("Must specify either existing_cluster_id or new_cluster.")
         return run_json
 
-    def launch_notebook_job(self) -> str:
+    def launch_notebook_job(self) -> int:
         run_json = self._get_run_json()
         self.databricks_run_id = self._hook.submit_run(run_json)
         url = self._hook.get_run_page_url(self.databricks_run_id)
@@ -1033,6 +1036,8 @@ def launch_notebook_job(self) -> str:
         return self.databricks_run_id
 
     def monitor_databricks_job(self) -> None:
+        if self.databricks_run_id is None:
+            raise ValueError("Databricks job not yet launched. Please run launch_notebook_job first.")
         run = self._hook.get_run(self.databricks_run_id)
         run_state = RunState(**run["state"])
         self.log.info("Current state of the job: %s", run_state.life_cycle_state)
@@ -1059,4 +1064,5 @@ def monitor_databricks_job(self) -> None:
 
     def execute(self, context: Context) -> None:
         self.launch_notebook_job()
-        self.monitor_databricks_job()
+        if self.wait_for_termination:
+            self.monitor_databricks_job()
diff --git a/tests/providers/databricks/operators/test_databricks.py b/tests/providers/databricks/operators/test_databricks.py
index 0f70f7f7fe1c9..902aa37e918ea 100644
--- a/tests/providers/databricks/operators/test_databricks.py
+++ b/tests/providers/databricks/operators/test_databricks.py
@@ -1758,23 +1758,41 @@ def test_databricks_run_now_deferrable_operator_success_before_defer(self, mock_
 
 
 class TestDatabricksNotebookOperator:
-    def test_execute(self):
+    def test_execute_with_wait_for_termination(self):
         operator = DatabricksNotebookOperator(
             task_id="test_task",
             notebook_path="test_path",
             source="test_source",
             databricks_conn_id="test_conn_id",
         )
-        operator.launch_notebook_job = MagicMock(return_value="12345")
+        operator.launch_notebook_job = MagicMock(return_value=12345)
         operator.monitor_databricks_job = MagicMock()
 
         operator.execute({})
 
+        assert operator.wait_for_termination is True
         operator.launch_notebook_job.assert_called_once()
         operator.monitor_databricks_job.assert_called_once()
 
+    def test_execute_without_wait_for_termination(self):
+        operator = DatabricksNotebookOperator(
+            task_id="test_task",
+            notebook_path="test_path",
+            source="test_source",
+            databricks_conn_id="test_conn_id",
+            wait_for_termination=False,
+        )
+        operator.launch_notebook_job = MagicMock(return_value=12345)
+        operator.monitor_databricks_job = MagicMock()
+
+        operator.execute({})
+
+        assert operator.wait_for_termination is False
+        operator.launch_notebook_job.assert_called_once()
+        operator.monitor_databricks_job.assert_not_called()
+
     @mock.patch("airflow.providers.databricks.operators.databricks.DatabricksHook")
-    def test_monitor_databricks_job_successful(self, mock_databricks_hook):
+    def test_monitor_databricks_job_successful_raises_no_exception(self, mock_databricks_hook):
         mock_databricks_hook.return_value.get_run.return_value = {
             "state": {"life_cycle_state": "TERMINATED", "result_state": "SUCCESS"}
         }
@@ -1786,13 +1804,13 @@ def test_monitor_databricks_job_successful(self, mock_databricks_hook):
             databricks_conn_id="test_conn_id",
         )
 
-        operator.databricks_run_id = "12345"
+        operator.databricks_run_id = 12345
         operator.monitor_databricks_job()
 
     @mock.patch("airflow.providers.databricks.operators.databricks.DatabricksHook")
     def test_monitor_databricks_job_failed(self, mock_databricks_hook):
         mock_databricks_hook.return_value.get_run.return_value = {
-            "state": {"life_cycle_state": "TERMINATED", "result_state": "FAILED"}
+            "state": {"life_cycle_state": "TERMINATED", "result_state": "FAILED", "state_message": "FAILURE"}
         }
 
         operator = DatabricksNotebookOperator(
@@ -1802,9 +1820,12 @@ def test_monitor_databricks_job_failed(self, mock_databricks_hook):
             databricks_conn_id="test_conn_id",
         )
 
-        operator.databricks_run_id = "12345"
-        with pytest.raises(AirflowException):
+        operator.databricks_run_id = 12345
+
+        exception_message = "'Task failed. Final state %s. Reason: %s', 'FAILED', 'FAILURE'"
+        with pytest.raises(AirflowException) as exc_info:
             operator.monitor_databricks_job()
+        assert exception_message in str(exc_info.value)
 
     @mock.patch("airflow.providers.databricks.operators.databricks.DatabricksHook")
     def test_launch_notebook_job(self, mock_databricks_hook):
@@ -1815,11 +1836,11 @@ def test_launch_notebook_job(self, mock_databricks_hook):
             databricks_conn_id="test_conn_id",
             existing_cluster_id="test_cluster_id",
         )
-        operator._hook.submit_run.return_value = "12345"
+        operator._hook.submit_run.return_value = 12345
 
         run_id = operator.launch_notebook_job()
 
-        assert run_id == "12345"
+        assert run_id == 12345
 
     def test_both_new_and_existing_cluster_set(self):
         operator = DatabricksNotebookOperator(
@@ -1830,8 +1851,10 @@ def test_both_new_and_existing_cluster_set(self):
             existing_cluster_id="existing_cluster_id",
             databricks_conn_id="test_conn_id",
         )
-        with pytest.raises(ValueError):
+        with pytest.raises(ValueError) as exc_info:
             operator._get_run_json()
+        exception_message = "Both new_cluster and existing_cluster_id are set. Only one should be set."
+        assert str(exc_info.value) == exception_message
 
     def test_both_new_and_existing_cluster_unset(self):
         operator = DatabricksNotebookOperator(
@@ -1840,8 +1863,10 @@ def test_both_new_and_existing_cluster_unset(self):
             source="test_source",
             databricks_conn_id="test_conn_id",
         )
-        with pytest.raises(ValueError):
+        with pytest.raises(ValueError) as exc_info:
             operator._get_run_json()
+        exception_message = "Must specify either existing_cluster_id or new_cluster."
+        assert str(exc_info.value) == exception_message
 
     def test_job_runs_forever_by_default(self):
         operator = DatabricksNotebookOperator(
@@ -1864,5 +1889,10 @@ def test_zero_execution_timeout_raises_error(self):
             existing_cluster_id="existing_cluster_id",
             execution_timeout=timedelta(seconds=0),
         )
-        with pytest.raises(ValueError):
+        with pytest.raises(ValueError) as exc_info:
             operator._get_run_json()
+        exception_message = (
+            "If you've set an `execution_timeout` for the task, ensure it's not `0`. "
+            "Set it instead to `None` if you desire the task to run indefinitely."
+        )
+        assert str(exc_info.value) == exception_message