diff --git a/providers/ssh/src/airflow/providers/ssh/operators/ssh.py b/providers/ssh/src/airflow/providers/ssh/operators/ssh.py
index e6e90f50d765c..8f22a86407137 100644
--- a/providers/ssh/src/airflow/providers/ssh/operators/ssh.py
+++ b/providers/ssh/src/airflow/providers/ssh/operators/ssh.py
@@ -24,8 +24,8 @@
 
 from airflow.configuration import conf
 from airflow.exceptions import AirflowException, AirflowSkipException
-from airflow.models import BaseOperator
 from airflow.providers.ssh.hooks.ssh import SSHHook
+from airflow.providers.ssh.version_compat import BaseOperator
 from airflow.utils.types import NOTSET, ArgNotSet
 
 if TYPE_CHECKING:
diff --git a/providers/ssh/src/airflow/providers/ssh/version_compat.py b/providers/ssh/src/airflow/providers/ssh/version_compat.py
new file mode 100644
index 0000000000000..4f8d5e32bca4a
--- /dev/null
+++ b/providers/ssh/src/airflow/providers/ssh/version_compat.py
@@ -0,0 +1,42 @@
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements.  See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership.  The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License.  You may obtain a copy of the License at
+#
+#   http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied.  See the License for the
+# specific language governing permissions and limitations
+# under the License.
+#
+# NOTE! THIS FILE IS COPIED MANUALLY IN OTHER PROVIDERS DELIBERATELY TO AVOID ADDING UNNECESSARY
+# DEPENDENCIES BETWEEN PROVIDERS. IF YOU WANT TO ADD CONDITIONAL CODE IN YOUR PROVIDER THAT DEPENDS
+# ON AIRFLOW VERSION, PLEASE COPY THIS FILE TO THE ROOT PACKAGE OF YOUR PROVIDER AND IMPORT
+# THOSE CONSTANTS FROM IT RATHER THAN IMPORTING THEM FROM ANOTHER PROVIDER OR TEST CODE
+#
+from __future__ import annotations
+
+
+def get_base_airflow_version_tuple() -> tuple[int, int, int]:
+    from packaging.version import Version
+
+    from airflow import __version__
+
+    airflow_version = Version(__version__)
+    return airflow_version.major, airflow_version.minor, airflow_version.micro
+
+
+AIRFLOW_V_3_0_PLUS = get_base_airflow_version_tuple() >= (3, 0, 0)
+
+if AIRFLOW_V_3_0_PLUS:
+    from airflow.sdk import BaseOperator
+else:
+    from airflow.models import BaseOperator  # type: ignore[no-redef]
+
+__all__ = ["AIRFLOW_V_3_0_PLUS", "BaseOperator"]
diff --git a/providers/ssh/tests/unit/ssh/operators/test_ssh.py b/providers/ssh/tests/unit/ssh/operators/test_ssh.py
index 06ea865fc4481..b100fc13d31a4 100644
--- a/providers/ssh/tests/unit/ssh/operators/test_ssh.py
+++ b/providers/ssh/tests/unit/ssh/operators/test_ssh.py
@@ -268,7 +268,7 @@ def test_push_ssh_exit_to_xcom(self, request, dag_maker):
         dr = dag_maker.create_dagrun(run_id="push_xcom")
         ti = TaskInstance(task=task, run_id=dr.run_id)
         with pytest.raises(AirflowException, match=f"SSH operator error: exit status = {ssh_exit_code}"):
-            ti.run()
+            dag_maker.run_ti("push_xcom", dr)
         assert ti.xcom_pull(task_ids=task.task_id, key="ssh_exit") == ssh_exit_code
 
     def test_timeout_triggers_on_kill(self, request, dag_maker):
@@ -278,18 +278,17 @@ def command_sleep_forever(*args, **kwargs):
         self.exec_ssh_client_command.side_effect = command_sleep_forever
 
         with dag_maker(dag_id=f"dag_{request.node.name}"):
-            task = SSHOperator(
+            _ = SSHOperator(
                 task_id="test_timeout",
                 ssh_hook=self.hook,
                 command="sleep 100",
                 execution_timeout=timedelta(seconds=1),
             )
         dr = dag_maker.create_dagrun(run_id="test_timeout")
-        ti = TaskInstance(task=task, run_id=dr.run_id)
 
         with mock.patch.object(SSHOperator, "on_kill") as mock_on_kill:
             with pytest.raises(AirflowTaskTimeout):
-                ti.run()
+                dag_maker.run_ti("test_timeout", dr)
 
             # Wait a bit to ensure on_kill has time to be called
             time.sleep(1)