Left-back Charlie Mulgrew scored twice and set up Glenn Loovens and Gary Hooper for two more before Joe Ledley and Hooper added the gloss as Neil Lennon's side gained revenge on Kilmarnock for last month's League Cup final defeat.
Celtic, also in the semi-final of the Scottish Cup against Hearts next weekend, lead bitter foes Rangers by an unassailable 18 points with five games left. Rangers beat St Mirren 3-1.
"It's the best day of my professional life. It's been a long time coming," Lennon, long subject of sectarian abuse from Rangers fans, told reporters.
"It's been two years in the waiting. I'm so proud of them. They deserve it. We have been the best team in Scotland by a long way and we have finished it in the right way."
Celtic's next home game is against Rangers but it has already been decided they will receive the league trophy on another occasion in order not to inflame tensions.
The "Hoops", who will enter the Champions League third qualifying round next term, could have won the title at Rangers last month but a 3-2 win for Ally McCoist's side at least gave the home fans a modicum of cheer.
Administrators are considering three bids for Rangers and hope to announce the acceptance of one offer next week.
The utter dominance of the Glasgow duo over Scottish football means Rangers are still likely to finish second despite their points deduction.
