Neil Lennon's men finished the campaign 29 points ahead of the second-placed Motherwell with their latest success.
The win – Celtic's 31st of the season – came despite an arm-wrestle that lasted more than an hour in Glasgow.
Anthony Stokes eventually opened the scoring in the 64th minute before substitute Giorgos Samaras doubled their lead from the penalty spot.
A Filip Twardzik own goal 11 minutes from the end set up a nervy finish but Kris Commons was on hand to wrap up the win for Celtic.
It was fitting that Commons scored the decisive goal, his 27th of the season, as the attacker finished as the league's top scorer.
Celtic were then presented with the trophy as their players and fans begun celebrations in the Scottish capital.
Other results on Sunday saw Motherwell finish second after a 1-0 win at Aberdeen.
Craig Reid scored the game's only goal in the 93rd minute, as Motherwell leapfrogged their opponents.
Both sides will take part in next season's UEFA Europa League qualifying.
And Inverness Caledonian Thistle moved into fifth after a 2-0 home win over St. Johnstone, which came thanks to goals from Ryan Christie and Greg Tansey.
