Following Alex Cochrane's first-half dismissal, goals in the second half from Kyogo Furuhashi and Oh Hyeon-gyu, the former netting his 50th for the Hoops, were enough to seal maximum points for Ange Postecoglou's side and secure their 53rd top-flight title with four games to spare.
The Hoops arrived at Tynecastle knowing that victory would be enough to secure their 11th Premiership title in 12 seasons, regardless of the result between second-placed Rangers and Aberdeen at Ibrox.
Hearts threatened to spoil Celtic's party after making a bright start to the contest, but Celtic gradually grew into the game before a controversial VAR decision gave the Hoops a major boost on the stroke of half time.
Cochrane was initially handed a yellow card for clipping the heels of Daizen Maeda on the edge of the area, but the decision was eventually upgrade to a red, as on-field referee Nick Walsh deemed the Jam Tarts defender to have denied a goalscoring opportunity following a consultation with VAR at the pitchside monitor.
Following a first half without a single shot on target from either team, Celtic struggled to break down Hearts after the interval, but if anyone was going to break the deadlock for Celtic it would be star forward Furuhashi.
The Japan international, who had scored in each of his previous six meetings with Hearts, managed to squeeze the ball in at the near post on the 67-minute mark to open the scoring, expertly flicking the ball beyond Zander Clark after receiving a low-driven cross from the right by Reo Hatate.
More to follow.