The Spanish side produced a magnificent display at the Allianz Arena on Tuesday to bring Bayern's title defence to an emphatic end with a 5-0 aggregate victory.
Real - who beat Bayer Leverkusen in their last final appearance 12 years ago - took a giant step towards a long-awaited 10th success in Europe's premier club competition courtesy of braces from Sergio Ramos and Cristiano Ronaldo.
Leading 1-0 from last week's first leg, Ramos' early double put Real in control of the tie, before Ronaldo settled the tie in the 34th minute with a strike that broke the record for most Champions League goals in a season.
Real will now face Chelsea or city rivals Atletico Madrid in next month's final in Lisbon, and their hopes of a treble in Carlo Ancelotti's first season at the Bernabeu remain very much alive.
But it did not take long for Ancelotti's men to make the crucial breakthrough, which came in the 16th minute when the unmarked Ramos met Luka Modric's perfectly placed corner with a bullet header.
And just four minutes later, Real doubled that advantage to take control of the tie as Pepe flicked Angel di Maria's right-wing free-kick towards Ramos, who netted his second goal of the game with a diving header.
Bayern did finally threaten the Real goal midway through the first half, Franck Ribery flashing an effort across the face of goal, but the visitors’ threat on the counter was perfectly illustrated shortly after by a fine break from Ronaldo, although the Portuguese could only fire wide from the edge of the area.
Arjen Robben curled an effort narrowly wide from the edge of the area, before Toni Kross lashed a decent effort just over the bar.
However, a miserable night for Bayern coach Pep Guardiola was capped off in the 90th minute, as Ronaldo drove a low 20-yard free-kick under the wall for his 16th Champions League goal of the campaign that ends Bayern's chances of winning a second straight treble.
