Brendan Rodgers's side could have wrapped up the title without kicking a ball on Tuesday night, but Rangers' comeback from two goals down to beat Dundee 5-2 delayed their coronation.
However, starting the day three points above the Gers, Celtic only required a draw at Kilmarnock to ensure their status as Scotland's top dogs, but they sealed their third straight crown in style.
Adam Idah started the goal rush in the fifth minute, before Daizen Maeda doubled Celtic's lead with 12 minutes gone and James Forrest put the champions three up before the break.
A second-half double from Matt O'Riley put the result beyond any doubt, and Celtic have now won the title in 12 of the last 13 seasons, the outlier being Rangers' success in the 2020-21 season.
Rodgers's side will conclude their triumphant campaign at home to St Mirren on Saturday, before attempting to complete the double when they clash with Old Firm rivals Rangers in the Scottish Cup final on May 25.
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