Dundee will be playing Championship football next season as they drop out after St Johnstone beat Aberdeen.
Mark McGhee 's side beat Hibs on Tuesday night in their first win since the new boss took over.
That asked the question of the Perth Saints who needed just one more point to secure 11th placed.
But they took all three on Wednesday and that was enough to relegate Dundee.
They were last relegated to the Championship at the end of the 2018-19 season.
And they have failed to maintain their top flight status after gaining promotion through the play-offs under James McPake at the end of the 2020-21 campaign.
Their last win remains a Scottish Cup success at Peterhead under the former boss.
St Johnstone's win meanwhile wasn't enough to spare them from the potential trapdoor of the play-off – where they'll meet either Inverness or Arbroath.
