Neil Lennon's side only needed a draw to become champions for the eighth season in a row but they claimed all three points with an emphatic win at Pittodrie.
Mikael Lustig opened the scoring with a diving header five minutes before half-time and fellow defender Jozo Simunovic added a second goal early in the second half. Odsonne Edouard wrapped things up with a late third for the visitors.
Celtic will be presented with the trophy after their final game of the season against Hearts on Sunday May 19, live on Sky Sports at 3.00pm.
Elsewhere in the Ladbrokes Premiership today, Dundee were relegated after a 1-0 home defeat to Hamilton Accies, who are now four points clear of a St Mirren side who drew 1-1 at Motherwell.
Kilmarnock are up to third place thanks to a 1-0 win over Hearts at Tynecastle and it was 1-1 between St Johnstone and Livingston at McDiarmid Park.