Daniel MacKay pulled a goal back late on before Jota sealed the 3-1 victory with a thumping finish.
After winning thew League Cup earlier this year and completing their defence of the Premiership title, the victory sealed the treble and underlined Celtic’s position at the top of the game in Scotland this season.
Prior to kick-off, Celtic were boosted by the news that Kyogo Furuhashi and Alistair Johnston were fit to start after picking up knocks in the final Premiership game against Aberdeen last week. Inverness had endured a long wait since the end of their league campaign four weeks ago but had tried to keep their sharpness through bounce games in preparation.
After kick off in the sunshine at Hampden, Celtic were on the front foot right away but Inverness were compact and well-disciplined, working to restrict the league champions to minimal chances.
The game plan proved effective in the early stages, with Celtic failing to find their usual rhythm and unable to find a way through the packed Inverness defence.
The resistance had lasted through the opening half hour but a moment of quality in the 37th minute brought the opening Postecoglou’s side had been waiting for.
A low pass was slid in to Matt O’Riley, who had burst into the Inverness box. He looked up and picked out Kyogo who finished first time with trademark accuracy.
Having taken the lead, Celtic poured forward in search of more and Kyogo nearly had his second goal three minutes later, finding space in the box to collect a Reo Hatate pass but lifting his shot wide.
Inverness then picked up the first booking of the game, David Carson seeing a yellow card for kicking the ball at Jota as the Celtic player lay on the ground after being fouled.
Just one goal separated the side at the break but there was no doubt Dodds had the tougher team talk, having seen his side undone at the back and not managing to pose much threat to the Celtic goal.
Celtic made a change at the break, bringing Liel Abada on for Daizen Maeda, and looked to press home their advantage.
The game followed a similar pattern, with Celtic having plenty of the ball but struggling to find the incisive final pass. Just before the hour mark Kyogo was withdrawn and replaced by Hyeongyu Oh.
If Inverness thought that Kyogo’s withdrawal might dull the threat they were mistaken. In the 64th minute, Callum McGregor played the ball out to Jota on the left, burst into the box for the return ball and then played it across goal for Abada to stab into the back of the net.
A VAR review meant the Celtic fans had to wait to celebrate but when it confirmed the 2-0 lead, Hampden erupted as Celtic closed in on the trophy.
They almost had a third to celebrate ten minutes later when a mistake from Ridgers gave Celtic possession but the Inverness keeper was equal to O’Riley’s stinging shot.
Both sides made changes in the latter stages but Inverness were unable to change the balance of play against a team that had seen off opposition in all three competitions this season.
Just as Celtic’s victory began to look inevitable. With six minutes left on the clock, Inverness gave themselves hope.
Wallace Duffy got forward to fire in a cross and Daniel MacKay stooped to head past Joe Hart.
The goal energised the underdogs but also sharpened Celtic’s resolve and just after six minutes of additional time were added, Celtic restored their two-goal advantage.
Sead Haksabanovic had just gone close with a shot after a McGregor pass when Celtic got forward again. Abada hit the byline and delivered a perfect cross that Jota took on his chest before blasting into the net.
All that was left for the final minutes to tick down and Celtic celebrated winning the trophy and completing their domination of domestic trophies this season.