Having already masterminded the Bhoys' triumphs in the Scottish Premiership and Scottish League Cup, Ange Postecoglou witnessed his side get off to a slow start, but goals from Kyogo Furuhashi, Liel Abada and Jota sealed the deal against Caley Thistle, who registered through Daniel MacKay's late header.
Perhaps affected by the ongoing speculation surrounding their manager, who is thought to be the leading candidate for the Tottenham Hotspur job, Celtic struggled to assert their dominance in the early exchanges.
While unsurprisingly enjoying the lion's share of possession, Postecoglou's men could only fashion a few half-chances, as the Caley Thistle backline defended with vigour to keep the Bhoys at bay.
However, the prolific Furuhashi needed just one sight of goal to make a difference, and Celtic belatedly broke Inverness' resistance with 38 minutes on the clock.
Picking up the ball on the right-hand side of the box, Matt O'Riley burst towards the byline and cut back for Furuhashi, who made an intelligent run to the near post to drill a first-time strike into the roof of the net.
The Japanese striker brought up goal number 34 for the season with the game's opener, and he could have registered number 35 just three minutes later as he latched onto Reo Hatate's pass, but his attempt at an outside-of-the-boot finish went horribly wrong as he fired wide of the post.
The second half began in a similar vein to the first, with Celtic biding their time and trying to find gaps in the Caley Thistle backline - initially to little effect - but the Championship side were also struggling for inspiration in their search of an equaliser.
Postecoglou's side eventually wore Inverness down a second time in the 65th minute, as Callum McGregor squared for Abada to tap in from a few yards out, and the goal was confirmed following a lengthy VAR review for a possible offside offence.
The Celtic contingent in attendance would have surely been expecting a simple stroll to the finish line, as Inverness remained out of ideas in attack and gave Joe Hart very little to think about.
However, it would ostensibly be anything but a simple stroll, as in the 84th minute, Wallace Duffy sent in a peach of a cross from the right flank, and MacKay's bullet header flew past Hart to give Billy Dodds's men a slice of hope.
That slice of hope would last just seven minutes, though, as in the start of added time, Abada's deep cross to the back post found Jota, who chested the ball down and found the far corner through three Caley Thistle bodies to restore Celtic's two-goal cushion, and the treble party soon began for the boys in white and green.
Celtic now have a staggering 41 Scottish Cup titles to their name, while Inverness suffered their first-ever final defeat, having beaten Falkirk in their only previous appearance in the showpiece match in 2015.