Immediately afterwards, Celtic offered manager Neil Lennon the job permanently. Lennon said there's "a good chance" he'll accept.
Lennon was asked by Celtic to take charge in February to the end of the season when Brendan Rodgers left to join English Premier League team Leicester.
In his second stint with Celtic, Lennon helped them win the premiership and League Cup titles.
Celtic chief executive Peter Lawwell said Lennon would have been offered the job whatever the result of the cup final. He wanted to end speculation now. He hoped to work out the contract details this week.
"Neil stepped up to the plate when we needed him," Lawwell wrote on the club's Twitter account.
So did striker Odsonne Edouard in the final at Hampden Park as Celtic rallied.
After an absorbing but goalless first half, Ryan Edwards struck from close range in the 52nd minute to put Hearts ahead.
Edouard leveled with a penalty just after the hour mark, and fired in the dramatic winner with eight minutes remaining.
The "triple treble," as it is being called in Scotland, highlights Celtic's domestic domination despite a change of managers.
Lennon helped Celtic finish off an eighth successive premiership title with two games to spare, and win a third successive League Cup.
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