diff --git a/airflow-core/src/airflow/configuration.py b/airflow-core/src/airflow/configuration.py
index 4c66ba6792004..ac9eea5273331 100644
--- a/airflow-core/src/airflow/configuration.py
+++ b/airflow-core/src/airflow/configuration.py
@@ -777,6 +777,7 @@ def validate(self):
                     )
 
         self._upgrade_postgres_metastore_conn()
+        self._strip_trailing_slash_from_base_url()
         self.is_validated = True
 
     def _upgrade_postgres_metastore_conn(self):
@@ -808,6 +809,19 @@ def _upgrade_postgres_metastore_conn(self):
             old_env_var = self._env_var_name("core", key)
             os.environ.pop(old_env_var, None)
 
+    def _strip_trailing_slash_from_base_url(self):
+        """Validate that api base_url config does not end with `/`."""
+        key = "base_url"
+        base_url = self.get("api", key, fallback="")
+        if base_url and base_url.endswith("/"):
+            self.upgraded_values[("api", key)] = base_url
+            new_base_url = base_url.rstrip("/")
+            self._update_env_var(section="api", name=key, new_value=new_base_url)
+        # if the old value is set via env var, we need to wipe it
+        # otherwise, it'll "win" over our adjusted value
+        old_env_var = self._env_var_name("core", key)
+        os.environ.pop(old_env_var, None)
+
     def _validate_enums(self):
         """Validate that enum type config has an accepted value."""
         for (section_key, option_key), enum_options in self.enums_options.items():
diff --git a/airflow-core/src/airflow/models/taskinstance.py b/airflow-core/src/airflow/models/taskinstance.py
index 8b690b417e1ef..eeb2321ec1e4c 100644
--- a/airflow-core/src/airflow/models/taskinstance.py
+++ b/airflow-core/src/airflow/models/taskinstance.py
@@ -616,10 +616,10 @@ def to_runtime_ti(self, context_from_server) -> RuntimeTaskInstanceProtocol:
     def log_url(self) -> str:
         """Log URL for TaskInstance."""
         run_id = quote(self.run_id)
-        base_url = conf.get("api", "base_url", fallback="http://localhost:8080/")
+        base_url = conf.get("api", "base_url", fallback="http://localhost:8080")
         map_index = f"/mapped/{self.map_index}" if self.map_index >= 0 else ""
         try_number = f"?try_number={self.try_number}" if self.try_number > 0 else ""
-        _log_uri = f"{base_url}dags/{self.dag_id}/runs/{run_id}/tasks/{self.task_id}{map_index}{try_number}"
+        _log_uri = f"{base_url}/dags/{self.dag_id}/runs/{run_id}/tasks/{self.task_id}{map_index}{try_number}"
 
         return _log_uri