diff --git a/.changes/unreleased/Under the Hood-20240215-151417.yaml b/.changes/unreleased/Under the Hood-20240215-151417.yaml
new file mode 100644
index 000000000..608e10d05
--- /dev/null
+++ b/.changes/unreleased/Under the Hood-20240215-151417.yaml	
@@ -0,0 +1,6 @@
+kind: Under the Hood
+body: Add `session_id` to `SnowflakeAdapterResponse`
+time: 2024-02-15T15:14:17.873819247+01:00
+custom:
+  Author: jeppe742
+  Issue: "881"
diff --git a/dbt/adapters/snowflake/connections.py b/dbt/adapters/snowflake/connections.py
index 6b325ab9c..2eef68131 100644
--- a/dbt/adapters/snowflake/connections.py
+++ b/dbt/adapters/snowflake/connections.py
@@ -85,6 +85,7 @@ def snowflake_private_key(private_key: RSAPrivateKey) -> bytes:
 @dataclass
 class SnowflakeAdapterResponse(AdapterResponse):
     query_id: str = ""
+    session_id: str = ""
 
 
 @dataclass
@@ -444,7 +445,8 @@ def get_response(cls, cursor) -> SnowflakeAdapterResponse:
             rows_affected=cursor.rowcount,
             code=code,
             query_id=cursor.sfqid,
-        )
+            session_id=str(cursor.connection.session_id)
+        )  # type: ignore
 
     # disable transactional logic by default on Snowflake
     # except for DML statements where explicitly defined
diff --git a/tests/functional/artifacts/test_run_results.py b/tests/functional/artifacts/test_run_results.py
new file mode 100644
index 000000000..345d06d8a
--- /dev/null
+++ b/tests/functional/artifacts/test_run_results.py
@@ -0,0 +1,18 @@
+import pytest
+from dbt.tests.util import run_dbt
+
+good_model_sql = """
+select 1 as id
+"""
+
+
+class TestRunResultsSuccess:
+    @pytest.fixture(scope="class")
+    def models(self):
+        return {"model.sql": good_model_sql}
+
+    def test_adapter_response_exists(self, project):
+        results = run_dbt(["run"])
+        assert len(results.results) == 1
+        assert results.results[0].adapter_response["query_id"].strip() != ""
+        assert results.results[0].adapter_response["session_id"].strip() != ""