The Hoops went into the game only needing a point but they did not come to life until after a dull, goalless first half when a Gary Hooper double and a strike by stand-in skipper Joe Ledley in between, got the celebrations fully under way.
Georgios Samaras, on for Anthony Stokes, completed the scoring for Celtic with a virtuoso goal two minutes from time as Aaron Doran netted an even later consolation for the visitors.
Celtic can now look forward to the William Hill Scottish Cup final against Hibernian at Hampden next month, where they will try to complete the domestic double. Combined with a run to the Champions League last 16, that would represent a fine campaign for Neil Lennon and his side.
The Hoops boss made one change with Stokes, who scored the winner in last week's Scottish Cup semi-final win over Dundee United, replacing Emilio Izaguirre who started on the bench.
Caley boss Terry Butcher, whose side had won here in November, brought back defender Gary Warren for Danny Devine, who was named among the substitutes.
Lennon watched from the stand, serving the first of a three-game ban after being found guilty of offensive language towards St Mirren skipper Jim Goodwin in a game at the end of March, and would have expected better in the first half in which side were a little sluggish.
In the 12th minute Stokes headed a Kris Commons corner over the crossbar, moments before midfielder Victor Wanyama somehow headed wide after right-back Mikael Lustig's cross from the right had the Inverness defence in a flap.
Wanyama's clever pass released Hooper in the 23rd minute but when he lobbed Caley goalkeeper Antonio Reguero there was time for Warren to race back to head over for a corner.
Almost 10 minutes later Stokes had the ball in the net but the flag was up several seconds beforehand to stifle the cheers.
There was a scare for the home side in the 37th minute when Graeme Shinnie's inswinging corner from the right was flicked on by Owain Tudur Jones before the ball flew out the other side of the box. That was enough to remind the home fans that the title was not yet won.
A minute before the break Stokes' angled drive sped past the far post and there were claims for a free-kick at the edge of the box when Inverness defender Josh Meekings prevented Hooper going through but referee Kevin Clancy ignored the furore before bringing the first half to a close.
Izaguirre replaced James Forrest for the start of the second half with Charlie Mulgrew moving into midfield and Devine came on for Warren five minutes after the restart.
Still the game refused to burst into life and there was some agitation in the stands and in the Celtic dugout which increased further when Hoops defender Efe Ambrose headed a Commons corner over the bar from close range in the 56th minute.
Four minutes later, however, Celtic got the breakthrough.
It was all too easy for Commons to play the ball into the box to Hooper, who held off Graeme Shinnie before driving low past the helpless Reguero from 12 yards.
That was the signal for the home side to push on and Ledley set up the overlapping Lustig before getting on the end of the return pass to guide the ball past Reguero and into the far corner of the net.
Celtic Park came to life as the home fans vociferously began the count down to the final whistle.
In the 70th minute, with Celtic piling forward looking for more goals, Reguero did well to parry Lustig's deflected cross-cum-shot from the right before the move ended with Wanyama blasting over the crossbar.
However, the hosts were not to be denied and three minutes later Hooper's fancy flick from Commons' driven cross from the left ended up behind Reguero for number three.
Celtic dropped their guard for a few moments, allowing Caley a couple of chances but Samaras finished the game in fine style with a solo effort which ended with him crashing a shot from a tight angle in off the crossbar. Doran's goal in the final seconds of injury time, as he capitalised on slack defending, was a mere footnote.
- Sports & Recreation
- Anthony Stokes
- Gary Hooper