Celtic's win means they leapfrog the Jambos and finish top of the table on 82 points, two above Hearts in second.
Martin O'Neill's side scored two late goals to secure the victory the Glasgow club needed to deny Derek McInnes' team a fairytale first title since 1960.
Hearts initially looked on course when Lawrence Shankland headed them in front two minutes before the break, but Celtic responded deep into first-half stoppage time as Arne Engels converted from the spot.
An increasingly tense second period seemed destined for a stalemate, a result that would have handed Hearts the title, but with three minutes remaining, Daizen Maeda bundled the ball home. The goal was initially disallowed for offside before a VAR review overturned the decision.
As Hearts pushed desperately for an equaliser, goalkeeper Alexander Schwolow joined an attack in the closing moments. The gamble backfired when Callum Osmand was left with a simple finish into an unguarded net with virtually the final kick.
The final whistle sparked celebrations among Celtic supporters, many of whom spilled onto the pitch, while Hearts were left to absorb another agonising near-miss.
