The Australian's team has lost just one game all season, winning 31 of 34 matches to date while accumulating 95 points along the way in another astonishing season.
It was a simple win in the end for Celtic after a tricky opening spell that saw Hearts come out of the blocks firing on all cylinders.
But the hosts' positive start was soon curtailed when the video assistant referee (VAR) decided to inject himself into the game.
Alex Cochrane was initially booked by the on-field referee for a clumsy contact with Daizen Maida as he chased a ball towards goal, a decision that caused no complaints from either side, but then VAR decided the referee should take a second look, and after doing so the yellow turned red and the game swung firmly in Celtic's favour.
It still took a lot to break down a solid Hearts rearguard, but once again it was Kyogo Furuhashi who netted the vital opener, neatly popping the ball into the net for his 50th Celtic goal, and 30th of a prolific season, to give the visitors the lead on 67 minutes.
After falling awkwardly upon scoring the goal, Kyogo was replaced by Oh Hyeon-gyu, and he was on hand to knock in an Aaron Mooy assist on 80 minutes to effectively seal the result and the title for Postecoglou's men.
The Hoops can now focus on going for a record points total of 107, which they will achieve if they win their remaining matches, and also winning the treble, which they will secure if they beat Inverness Caledonian Thistle in the Scottish Cup final on 4 June (AEST).