Hoops boss Neil Lennon has been under huge pressure this season, but his side made history at Hampden Park on Sunday.
The Glasgow giants made hard work of completing a fourth successive Scottish Premier League, Scottish Cup and Scottish League Cup clean sweep in a final that was pushed back due to the coronavirus pandemic.
They were level at 3-3 after extra-time, but the Championship leaders went down 4-3 on spot-kicks.
Kristoffer Ajer scored the winning penalty after Hearts duo Stephen Kingsley and Craig Wighton failed to beat Conor Hazard from 12 yards, with Craig Gordon having denied Celtic midfielder Ryan Christie.
Christie and Odsonne Edouard had given Lennon's side a 2-0 half-time lead, but Liam Boyce and Kingsley struck to force extra-time in an epic encounter.
Leigh Griffiths restored Celtic's lead and, although Josh Ginnelly brought the Edinburgh club level again, the Scottish champions were not to be denied a 12th domestic trophy in a row.
The Scottish Professional Football League (SPFL) announced on Monday the 2019-20 season could not be completed due to the coronavirus pandemic.
Celtic were crowned champions for a record-equalling ninth time in a row and Hearts were consigned to the Championship after the final standings were calculated on a points-per-game basis.
Hearts were four points adrift of second-bottom Hamilton Academical with eight games to play when the season was suspended in March amid the COVID-19 crisis.
The Edinburgh club will not go down without a fight and still harbour hopes that the league may be restructured so they will stay in the top flight.
A club statement said: "We have stated from the outset that we don't believe it is right that any club should be unfairly penalised because of the COVID-19 pandemic.
"It was previously indicated that league reconstruction would not generate enough support to pass a vote between member clubs. In recent days a number of positive talks have been held with both the SPFL and member clubs and this topic is currently being revisited.
"Hearts will shortly submit a member's resolution that we believe is a pragmatic solution to the issues the game currently faces and a way forward that the clubs can unite behind. It is our belief that this resolution, if supported, will provide an opportunity to avoid disproportionately disadvantaging - financially and otherwise - any club.
"This is possibly the final chance for our game to stand together, protect each other and not only survive but flourish in the aftermath of this terrible pandemic.
"Players from across all leagues have shown a desire for reconstruction and having already received support from some clubs we are hopeful that this resolution can positively progress Scottish football.
"As previously intimated the club has been taking legal advice throughout this process and are continuing to do so. We hope that the resolution being prepared will avoid the need to go down this route. Legal action would be both time consuming and expensive. However, the cost to the club of relegation would outweigh these considerations.
"To our supporters, we thank you for showing patience and continuing to back the club. We will continue to fight against what we believe is an unjust outcome."
The Scottish Professional Football League (SPFL) announced the 2019-20 campaign could not be completed due to the coronavirus pandemic following consultation with all 12 top-flight clubs.
Celtic retain their title after the final standings were calculated on a points-per-game basis, just as the Championship, League One and League Two tables were.
Neil Lennon's side were 13 points clear of arch-rivals Rangers, who had a game in hand, with eight matches to play when the season was halted in March amid the COVID-19 crisis.
Hearts drop into the Championship, having been four points adrift of second-bottom Hamilton Academical. Dundee United were previously crowned champions of the second tier.
Glasgow giants Celtic can celebrate being crowned champions of Scotland nine times in a row for a second time, having also achieved the feat under Jock Stein in the 1973-74 season.
SPFL chairman Murdoch MacLennan said: "Firstly, I would like to take this opportunity to officially congratulate Celtic on their achievement of winning the Premiership this season, and also to sincerely commiserate with Hearts on their relegation.
"We would all have rather seen the league season played out on pitches, in stadiums and in front of supporters.
"This is not the way anybody involved with Scottish football would have wanted to conclude the league season but, given the grave and unprecedented circumstances that we are facing, the board has agreed that it is the only practical way forward.
"COVID-19 has wreaked havoc on sporting competitions around the world and the repercussions will be felt for a long time.
"Scottish government restrictions and deep concerns for both player and spectator safety left the SPFL with no realistic option but to call the Premiership now and we thank the Premiership clubs for their support on this decision."
