The Bhoys managed to hold out relatively comfortably to secure an unprecedented third treble in as many years, a run of form which has now seen Neil Lennon installed as their permanent manager for next season.
Celtic chief executive Peter Lawwell said Lennon would have been offered the job whatever the result of the cup final.
"It's probably one of the best days of my life. They are immortal now".
Lennon replaced Brendan Rodgers - who departed for Leicester City - in February when the club had already won the Scottish League Cup, but he guided them to Scottish Premiership success before this weekend's triumph.
The win came via two goals from French striker Odsonne Edouard after Hearts midfielder Ryan Edwards opened the scoring in the second half.
FDA approves $2M medicine, most expensive ever
The genetic disease affects about one in every 10,000 births, with at least 50 percent to 70 percent diagnosed with Type I form. Even with the treatment, children do not gain normal muscle function and could still require wheelchairs and other support.