diff --git a/airflow/providers/google/cloud/hooks/bigquery.py b/airflow/providers/google/cloud/hooks/bigquery.py
index 0a279d95e5d332..dabc842dfd7536 100644
--- a/airflow/providers/google/cloud/hooks/bigquery.py
+++ b/airflow/providers/google/cloud/hooks/bigquery.py
@@ -1588,7 +1588,7 @@ def get_job(
         job_id: str,
         project_id: str = PROVIDE_PROJECT_ID,
         location: str | None = None,
-    ) -> CopyJob | QueryJob | LoadJob | ExtractJob | UnknownJob:
+    ) -> BigQueryJob | UnknownJob:
         """Retrieve a BigQuery job.
 
         .. seealso:: https://cloud.google.com/bigquery/docs/reference/v2/jobs
@@ -1596,8 +1596,8 @@ def get_job(
         :param job_id: The ID of the job. The ID must contain only letters (a-z, A-Z),
             numbers (0-9), underscores (_), or dashes (-). The maximum length is 1,024
             characters.
-        :param project_id: Google Cloud Project where the job is running
-        :param location: location the job is running
+        :param project_id: Google Cloud Project where the job is running.
+        :param location: Location where the job is running.
         """
         client = self.get_client(project_id=project_id, location=location)
         job = client.get_job(job_id=job_id, project=project_id, location=location)
@@ -2849,15 +2849,16 @@ def rowcount(self) -> int:
         return -1
 
     def execute(self, operation: str, parameters: dict | None = None) -> None:
-        """Execute a BigQuery query, and return the job ID.
+        """Execute a BigQuery query, and update the BigQueryCursor description.
 
         :param operation: The query to execute.
         :param parameters: Parameters to substitute into the query.
         """
         sql = _bind_parameters(operation, parameters) if parameters else operation
         self.flush_results()
-        self.job_id = self._run_query(sql)
-
+        job = self._run_query(sql)
+        self.job_id = job.job_id
+        self.location = self.location or job.location
         query_results = self._get_query_result()
         if "schema" in query_results:
             self.description = _format_schema_for_description(query_results["schema"])
@@ -2997,15 +2998,15 @@ def _run_query(
         self,
         sql,
         location: str | None = None,
-    ) -> str:
-        """Run job query."""
+    ) -> BigQueryJob:
+        """Run a job query and return the job instance."""
         if not self.project_id:
             raise ValueError("The project_id should be set")
 
         configuration = self._prepare_query_configuration(sql)
         job = self.hook.insert_job(configuration=configuration, project_id=self.project_id, location=location)
 
-        return job.job_id
+        return job
 
     def _prepare_query_configuration(
         self,
@@ -3357,7 +3358,7 @@ async def get_job_instance(
 
     async def _get_job(
         self, job_id: str | None, project_id: str = PROVIDE_PROJECT_ID, location: str | None = None
-    ) -> CopyJob | QueryJob | LoadJob | ExtractJob | UnknownJob:
+    ) -> BigQueryJob | UnknownJob:
         """
         Get BigQuery job by its ID, project ID and location.