City will play Inter Milan in Istanbul on June 10 when Pep Guardiola will get the chance to win European football's elite competition for the third time as a coach.
Bernardo scored in the 23rd and 37th minute at Etihad Stadium on Wednesday, with Eder Militao's own goal in the 76th and a stoppage-time strike from substitute Julian Alvarez sealing a 5-1 aggregate win.
City are aiming to lift the Champions League for the first time in their history and have advanced to the final for the second time in three seasons.
“It's a beautiful night for us,” diminutive Bernardo told BT Sport.
“We knew it was going to be tough but to beat this Madrid team 4-0 at home... it's a wonderful feeling to be in the final again.
“Hopefully, this time we can win it.”
Madrid were gunning for a record-extending 15th European Cup, but were totally dominated in the second leg after the first match at the Santiago Bernabeu ended 1-1.
Madrid defender Dani Carvajal said: “We played a rival who were better than us in this match - they pretty well overwhelmed us.”
City remain on track for a wonderful treble. They can wrap up the Premier League title this weekend and face an FA Cup final date with Manchester United on June 3.
Bernardo beat Thibaut Courtois at his near post to put City ahead after Erling Haaland had already forced two saves from the Madrid goalkeeper.
Toni Kroos then hit the bar for the visitors, but Bernardo struck again when heading in a rebound after Ilkay Gundogan's effort was blocked.
Madrid have been the comeback kings over the past two season - including in last year’s semi-final against City when going through 6-5 after extra time.
There was to be no repeat on this occasion, as Militao headed into his own net in the second half to end Madrid's hopes, before the late strike from Alvarez.
Guardiola twice won the Champions League when coach of Barcelona but has failed to add to that total at former club Bayern Munich or City.
His ongoing struggles with City have been difficult to explain.
While the quality of his team has rarely been in question over his seven years in charge, their temperament on Europe’s biggest stage has been.
On too many occasions they have fallen short when the pressure was on - losing to underdogs such as Monaco, Lyon and Tottenham.
They were in command for almost the entirety of the semi against Madrid last year, but still managed to lose after blowing a two-goal lead in the last few minutes at the Bernabeu.
That never looked likely on this occasion, however, as City provided further evidence that they are finally ready to lift the Champions League trophy.
AAP
