Neil Lennon has now led Celtic to a league and cup double after succeeding Brendan Rodgers mid-season and has been offered the manager’s job permanently.
His side overcame the setback of Ryan Edwards’ second-half strike.
Edouard equalised from the penalty spot before coolly hitting the winner.
The Edinburgh side fought hard for an equaliser of their own in the closing stages, but Celtic stood firm to establish a new mark of triumph in the history of Scottish football.
The final whistle brought an emotional response from Lennon on the touchline.
His claim to the manager’s role was based on his experience of leading the club to success during a previous spell, of being able to urge and cajole players to deliver the best of themselves during the uncertainty that followed Rodgers’ departure for Leicester – and this cup victory was built on the resilience of his players.
Edouard delivers devastating double
Celtic were forced into a period of reflection during the interval at Hampden. It was clear enough what Lennon thought of their first-half performance, as he hollered for his players to raise the tempo of their game.
Much of the lethargy was caused by the organisation and determination of Hearts, who brought a level of assertiveness to their game that belied the pre-game assumptions that they would struggle to compete at Hampden.
Christophe Berra and John Souttar were solid pillars of resistance at the back, the latter clearing from Edouard inside the penalty area then blocking a James Forrest shot.
Hearts were not at full strength – striker Uche Ikpeazu was on the bench while 16-year-old Aaron Hickey started only his second game for the club at left-back, having made his first start last week in the final Premiership game of the season against Celtic.
Craig Levein’s side fought valiantly, though, and took the lead when Arnaud Djoum’s shot broke to Sean Clare, who back-heeled the ball to Edwards to shoot first-time beyond Scott Bain.
As Celtic responded, Souttar stood firm again, clearing after Scott Brown burst into the penalty area and then stepping in to clear from Tom Rogic.
Hearts could not maintain Souttar’s flawless display. Zlamal hesitated as he left his line to close down Edouard inside the penalty area, then panicked and slid into the striker. Referee Willie Collum pointed to the spot and Edouard converted with confidence when Zlamal perhaps could have done better.
The striker remained unflustered when Berra was caught out of position and Mikael Lustig’s header sent the ball through for Edouard to chase, and he coolly lifted the ball beyond the Hearts keeper’s reach and into the net.
“No fouls, no fouls” shouted Lennon as his side tried to close the game out, conscious of Hearts’ threat at set-pieces. Celtic had the experience and the calmness to see themselves over the line.
‘Hearts stifled Celtic’ – analysis
The pressure on the Celtic players was evident from the start, as they looked nervous in the early stages and it was only after Hearts took the lead that an urgency entered their game.
Hearts were wonderfully well organised and ensured Celtic’s key players were not allowed to dictate the pace while stifling their creativity.
Craig Levein and his players may look back upon this as a missed opportunity but there are plenty of positives to take from the 90 minutes.
None more so than the performance of teenager Aaron Hickey at full back, who belied his youth and was more than a match for James Forrest.
Both squads will have major surgery in the summer, with many players leaving new faces arriving at both Tynecastle and Parkhead. Then the quest will begin once more for league and cup glory.