The former St Johnstone and Aberdeen boss has agreed a deal until 2023 and will take charge for the first time against Queen of the South at Palmerston on Saturday.
Rugby Park director Billy Bowie said: "Derek is one of the most highly-respected managers in Scottish football and we are thrilled that he’s agreed to join Kilmarnock.
“It was clear he shared our determination and ambition to bring success to our club - we look forward to working with him to achieve our goals for this season and beyond.”
