The victory, inspired by Gary Hooper's double, left second-placed Motherwell, who won 3-1 at Dundee United on Friday, 15 points behind the Glasgow club with only four games remaining.
Celtic, who have now amassed 44 Scottish league championships, have coasted to the title more easily than last year given old foes Rangers were demoted to the bottom tier before the season because of financial problems.
Rangers, a world record 54 times Scottish champions, won the fourth tier last month.
Celtic have 72 points from 34 matches and will go into the Champions League qualifying rounds next term hoping to better their achievement of reaching the last 16 this season.
Fans had to wait until the second half to start the party with third-placed Inverness stubbornly refusing to bow to their far more illustrious opponents.
The breakthrough came just past the hour mark when Hooper was played in by Kris Commons and produced a cool finish.
Five minutes later Joe Ledley swept in the second before Hooper's neat flick at the near post made the result safe.
Georgios Samaras added some late gloss with a fierce shot in off the crossbar and not even a late reply from Aaron Doran could dampen the celebrations.
Celtic's complete dominance of the Scottish Premier League has again sparked calls for the club to play in England to find greater competition.
England's Premier League will contain two Welsh sides next season after Cardiff City won promotion to join Swansea City.
Wales has its own league but a handful of clubs including the duo have long been permitted to play in England, unlike their Scottish counterparts.
