Brendan Rodgers' side, now 25 points clear of second placed Aberdeen, set a new Scottish top-flight record as the earliest ever champions after wrapping up first place with eight games still to play.
Sinclair struck twice in the first half before Stuart Armstrong and Patrick Roberts netted after the interval at Tynecastle.
Sinclair's third, via the penalty spot, put the seal on the 48th Scottish title triumph in Celtic's illustrious history.
Celtic are unbeaten in 30 league games this season, winning 28 times.
Having already won the Scottish League Cup and with a Scottish Cup semi-final date against Glasgow rivals Rangers looming, Celtic could land the domestic treble in former Liverpool boss Rodgers' first season in charge.
Aberdeen's 7-0 win over Dundee on Friday had delayed the title party and meant Celtic needed a win against Hearts to clinch the championship.
They burst out the traps and Callum McGregor had the ball in the net after just two minutes but the midfielder was offside when he was picked out by Sinclair.
Hearts recovered well and Jamie Walker fired wide from 20 yards before Isma Goncalves cut in from the left and tested Craig Gordon with a thumping strike that the keeper gathered at the second attempt.
However, two quick-fire goals from Celtic soon turned the game on its head.
Sinclair took out three defenders as he played a give-and-go with Roberts and then lashed in a fierce strike high into the roof of the net leaving Jack Hamilton with no chance in the 24th minute.
English winger Sinclair grabbed a second just three minutes later.
Only in the starting line-up due to an injury to French striker Moussa Dembele, Roberts was the provider this time.
He jinked past a challenge before playing a superbly weighted pass through to Sinclair, who took two touches before drilling a low effort past Hamilton.
Celtic had the ball in the net again in the 51st minute when a sliding Tasos Avlonitis diverted a low James Forrest into his own net, but an offside flag had gone up against Sinclair, who was waiting to tap home for his hat-trick.
The travelling Celtic support didn't have to wait long to celebrate again as Armstrong made it 3-0 in the 55th minute.
Kieran Tierney's ball from the left was dummied by McGregor allowing the Scottish midfielder the time and space to send an unstoppable strike into the bottom corner of the net from 20 yards.
Roberts got the goal his play deserved in the 61st minute.
The on-loan Manchester City star collected a pass at the edge of the box before sending a curling effort into the top corner of the net.
Sinclair sealed the win from the penalty spot in the 84th minute.
He won the spot-kick himself after he was brought down by Avlonitis and the 28-year-old expertly despatched his effort past Hamilton for his 21st of an impressive debut season in Scotland.
Elsewhere, Rangers' hopes of catching Aberdeen in the race for second spot were dealt a major blow as they were held to a 1-1 draw by Motherwell at Ibrox on Saturday.
Pedro Caixinha's side now trail the Dons by 10 points with just eight games remaining.