Scott Sinclair’s hat trick was the centrepiece of the victory. The 28-year-old struck twice in the first half before Stuart Armstrong and Patrick Roberts netted after the interval at Tynecastle.
Sinclair's third, via the penalty spot, put the seal on the club’s 48th Scottish title.
Celtic, who have already won the League Cup, are unbeaten in 30 league games this season. They are still in the hunt for a third trophy in the shape of the Scottish Cup and face Glasgow rivals Rangers in the semi-finals of the competition.
"The win probably typified how they've been for the majority of the season. The professionalism they've showed, the attitude and determination and style in which they've played," Rodgers said. "We knew it was going to be a tough game but the style and the intensity of our play was admirable.
"To win a pressure game like that as convincingly as we did is an absolutely remarkable achievement by the players."
Sinclair, who joined Celtic at the start of the season from the English side Aston Villa, added: "It was great. I think with the big games I enjoy the pressure. It's great to come away and win the championship."