The Parkhead side, also aiming for a quadruple domestic treble in this current period of domination, took the lead in the rearranged semi-final in the 18th minute through Ryan Christie before fellow attacker Mohamed Elyounoussi added a second just five minutes later.
The Dons had taken a point in a 3-3 Premiership draw between the teams at Pittodrie last Sunday but found Neil Lennon's side a different proposition in the almost constant Glasgow rain.
Celtic refused to allow Derek McInnes's side a glimmer of hope and in the end ran out comfortable winners.
The Parkhead side will play Hearts in the final at the national stadium on December 20, a repeat of the 2019 final which Celtic won 2-1.
And having now won 35 successive domestic cup ties the Hoops will be odds-on to extend that record against the Championship Jambos and make more history.
Lennon had some selection dilemmas before the game and he brought back French striker Odsonne Edouard and Israel defender Nir Bitton, both recently out with Covid-19 issues, while midfielder Tom Rogic replaced Olivier Ntcham as Scott Bain kept his place in goals.
Dons boss McInnes had to deal with the late withdrawal of wing-back Jonny Hayes and he replaced him with Matty Kennedy, with attackers Scott Wright and Sam Cosgrove also back.
The Dons actually got off to a decent start. Within a minute Kennedy had crossed for Cosgrove to head just wide and five minutes later Bitton blocked another back-post header from the Pittodrie striker for a corner that came to nothing.
But Celtic stepped up the pace and Dons keeper Joe Lewis made a double save from Edouard after he had combined with Christie.
In the 15th minute Aberdeen defender Ash Taylor skimmed a header from a Wright corner past the far post.
Three minutes later, however, Celtic went ahead.
Rogic knocked the ball inside to Christie and he came on to his left foot with time and space to send a glorious shot from 25 yards high past the diving Lewis.
The holders doubled their lead when Rogic's inviting cross from the left beat the Dons keeper with Elyounoussi forcing it in at the back post, despite the attentions of defender Andrew Considine, for his fourth goal in four games.
Celtic had surrendered a two-goal lead to draw 2-2 against Lille in the Europa League on Thursday night but few would have backed the Granite City side to rescue this game.
The slick-moving Hoops exercised good control but four minutes after the restart Wright robbed Bitton down the left and set up Cosgrove inside the box but his tame shot was easily saved by Bain.
It was no prelude to a storming comeback.
Aberdeen did apply some pressure – midfielder Lewis Ferguson drove high over the bar in the 73rd minute and Tommie Hoban headed a Ryan Hedges free-kick over the bar – but Bain was not being tested.
The final stages brought a slew of substitutes but Celtic ensured yet another cup final appearance as they look to win the trophy for the 40th time.