With time running out and Hearts closing in on a first title for 60 years, Daizen Maeda and Callum Osmand shattered the visitors who had needed only a draw to finish top.
When Osmand ran through to score into an empty goal with virtually the last kick of stoppage time, pandemonium ensued with delirious Celtic fans streaming onto the pitch.
It was the 14th time in 15 seasons that Celtic have won the title, but none have been as hard-earned as they had trailed Hearts in the standings since the start of October, but have been revitalised since Martin O'Neill returned as interim manager in January and finished with seven successive victories.
"This is the most special place on Earth," O'Neill, 74, who has now won four league titles with Celtic, including three in the early 2000s during a five-year reign, said on the pitch.
"This season has been mental," Celtic full back Kieran Tierney told Sky Sports. "It's unbelievable. We never give up and this team is the most mentally strong team I've ever been involved with. This is the best thing I've ever won."
For Celtic skipper Callum McGregor, it was his 11th Scottish title, and he paid tribute to O'Neill.
"He dragged us through time and time again," he said. "What a season. Everyone wrote us off."
Hearts despair
It was despair for Hearts, who suffered the same fate as 40 years ago when they also lost out on the final day to Celtic after losing to Dundee when they needed just a point.
For the first time since 1991, the Scottish title went to a final-day decider between the top two, and there was a cauldron-like Parkhead atmosphere.
The visitors controlled the first half and seemed on course for glory when an unmarked Lawrence Shankland headed them in front from a Stephen Kingsley corner in the 43rd minute.
But Celtic were level in first-half stoppage time when Alexandros Kyziridis was adjudged by VAR to have blocked a Tierney cross with his arm, and Arne Engels stepped up to score from the penalty spot.
Celtic piled forward as the final whistle approached, and soon after Kelechi Iheanacho hit the post, Maeda scored from close range, only for the offside flag to go up. After an agonising wait for a VAR check, the goal was allowed to stand.
Hearts, who led the table for 226 days since the start of October, tried to respond in stoppage time and in one last desperate effort, everyone went forward for a corner.
When the ball broke for Celtic, and with Hearts keeper Alexander Schwolow stranded, Osmand ran the ball half the length of the pitch towards a heaving sea of green fans to seal it.
It was a devastating day for Hearts, who were so close to becoming the first team other than Celtic or Rangers to win the Scottish title since Aberdeen in 1985.
They will look back, with some justification, to the controversial stoppage-time penalty that Celtic scored to beat Motherwell 3-2 on Wednesday -- a result that swung the odds back towards the Glasgow giants.
Had that game ended in a draw, Celtic would have required a victory by three goals on Saturday.