City has now reached the semifinal stage in each of the last three seasons and will play tournament specialist and reigning champion Real Madrid in the final four.
“I’m so happy for three years in a row to be in the Champions League semifinals,” City manager Pep Guardiola told reporters after the second leg at the Allianz Arena.
“In this competition, it is the details. In these two games, in the right moments, we were there.”
City all but ended the tie after the first leg last week, beating Bayern 3-0 at the Etihad Stadium.
Bayern did improve on its poor performance in the return fixture and wasted a number of chances in the early stages on Wednesday, notably when Leroy Sane dragged a shot wide in the 17th minute when he just had goalkeeper Ederson to beat.
But any hope of a dramatic Bayern comeback was dashed when Erling Haaland, who had missed an earlier penalty, gave City the lead.
The Norwegian striker pounced on a mistake by defender Dayot Upamecano to smash home a finish into the top corner of the net in the 57th minute – his 12th Champions League goal of the season.
The Bavarians did manage to get on the score sheet, though, with Joshua Kimmich leveling the second leg with a penalty in the 83rd minute.
But it was too little, too late for the German side and the gulf in class between the two teams was clear to see.
Bayern boss Thomas Tuchel insisted his team were underdogs going into the quarterfinal against the Premier League champion but said he was proud of the performances over the two legs.
However, Bayern has now crashed out of two cup competitions in two weeks having previously being beaten in the German Cup.
“I am very satisfied with both games against Manchester City and with the way we presented ourselves today,” Tuchel told reporters after the match.
“We were on par with what is currently the best team in Europe.
“There was a difference in self confidence and form. For the few chances we conceded in both matches, we were punished. I don’t think the scoreline reflects the tie.”
Milan derby in other semifinal
Elsewhere on Wednesday, Inter Milan drew 3-3 against Benfica to secure a 5-3 aggregate win to reach the semifinals.
The Italian side will face fierce city rival AC Milan for a place in the Champions League final where the winner will face either Manchester City or Real Madrid in Istanbul on June 10.
The semifinal first legs are set to kickoff on May 9 and 10 before the return fixtures on May 16 and 17.