The Serie A leaders never looked like letting slip a 2-0 advantage from the first leg, and tightened their grip on the tie when Mario Mandzukic put them ahead after 33 minutes.
Brazilian defender Dani Alves crashed in a superb second just before half-time.
Monaco’s 18-year-old forward Kylian Mbappe netted a consolation in the 69th minute as Massimiliano Allegri’s impressively organised Italian side booked their place at Cardiff’s Millennium Stadium on June 3.
Goalkeeper Gianluigi Buffon said Juve’s professional attitude was key last night.
He said: “If we’d taken to the pitch thinking we were already through we would have found it tough, we were ready to react to everything they threw at us.
“That’s how we got through. We’ve got to Cardiff — I won’t say it was our aim because getting to the final means nothing.
“I’m really happy because I’m in good shape. I can’t deny the fact that if we didn’t have a great team getting there wouldn’t be possible. Two years ago everyone thought it was my last final — but you have to believe in your dreams and believe in what you do.”
And yet, it might have been different.
Monaco, who were this season’s surprise contenders after coming through qualifying to reach the last four, almost got off to the perfect start when Mbappe knocked the ball past Buffon but his effort came back off a post and the offside flag meant it would not have counted anyway.
Despite their two-goal advantage, Juventus remained on the offensive as Mandzukic forced a smart save from Monaco keeper Danijel Subasic after being played into the left side of the penalty area.
Juve finally took the lead after 32 minutes and all but secured their place in the final.
Alves whipped the ball into the Monaco box from the right towards Mandzukic, whose header was saved before the Croatian lashed the rebound past Subasic.
Just before half-time, Juventus doubled their lead with a superb strike from Alves.
A corner was punched out by Subasic and as the ball dropped to Alves 25 yards from goal, the former Barcelona defender volleyed it into the net before taking the deserved plaudits of the Turin crowd.
With Juventus having done the job, the second half lacked much tempo.
Monaco netted a consolation after 69 minutes when Mbappe converted a cross from Joao Moutinho for what was an impressive sixth Champions League goal by the France youngster.
But the night belonged to the Old Lady.
Inter Milan have sacked coach Stefano Pioli after six months in charge.
Pioli, who replaced Frank de Boer in November on an 18-month deal, has paid for Inter’s poor recent form which has seen the Nerazzurri pick up just one point from their last six games.
Sunday’s 1-0 defeat at Genoa left Inter in seventh place in Serie A, and proved the final straw for the club’s board.
Buffon, Barzagli (Benatia 85), Bonucci, Chiellini, Dani Alves, Pjanic, Khedira (Marchisio 10), Alex Sandro, Dybala (Cuadrado 54), Higuain, Mandzukic.
Subasic, Raggi ,Glik, Jemerson, Sidibe, Mendy (Fabinho 55), Bakayoko (Germain 78), Joao Moutinho, Bernardo Silva (Lemar 69), Falcao, Mbappe-Lottin .
Bjorn Kuipers (Netherlands).