The majority inside Celtic Park were biting their nails when Lawrence Shankland gave Hearts the lead on the stroke of half-time, but Martin O'Neill's men quickly went down the other end to equalise from the penalty spot through Arne Engels.
In an incredibly tense second-half, the hosts grabbed the title-sealing goal minutes from time when Daizen Maeda tapped home Callum Osmand's cross.
Osmand then scored deep into added time to make sure of victory after Hearts committed bodies forward and left an open net, sparking jubilant scenes on the pitch, with thousands of supporters streaming on.
Only a victory was enough for Celtic to pip Hearts to the title on the final day, and they did so in the most dramatic circumstances, with manager O'Neill taking most of the plaudits for an incredible turnaround.
“It’s all about Martin O’Neill, magic Martin. How he has turned this around, I couldn’t tell you," Chris Sutton said on Sky Sports.
“Celtic have stuttered and spluttered this season but Martin has got the old Honda Civic roaring again. When it mattered, a magnificent seven wins on the trot to take Celtic over the line.
“You wouldn’t be human if you didn’t sympathise with Hearts, they have had a magnificent season. They have been top and held their own all the way.
"This may be Martin O'Neill's biggest ever success in management."
O'Neil returned to the club in January following Wilfried Nancy's disastrous short tenure in charge, and somehow inspired his side to a league title after being six points behind when he was appointed.