Brendan Rodgers has now made it five domestic trophies out of five since taking over from Ronny Deila in the summer of 2016.
He and his Celtic players will have the chance to clinch back-to-back domestic trebles when they take on Motherwell in the Scottish Cup final later this month.
Requiring a victory to secure the title against their biggest rivals, Celtic raced into an early lead with Odsonne Edouard opening the scoring.
The Frenchman netted again before James Forrest put the hosts three goals to the good before half-time.
Tom Rogic made it 4-0 just after half-time before Callum McGregor added a fifth five minutes later.