The Bundesliga club can become the first-ever side to win the tournament at its home ground as a penalty shootout win was enough to see them through to the showpiece
The Bavarians found themselves under the cosh straight away as Los Blancos tried to overturn the 2-1 deficit from the first leg. An early Cristiano Ronaldo brace set them on their way but Arjen Robben leveled the tie from the penalty spot just before the half-hour mark.
The affair turned cagey in the second half as neither side wanted to over commit and with extra time unable to separate the pair, the match went all the way to penalties.
Manuel Neuer saved shots from both Ronaldo and Kaka before Sergio Ramos skied it from 12 yards, allowing Bastian Schweinsteiger the chance to net the winning penalty.
Jose Mourinho made only one change from the side that defeated Barcelona at Camp Nou at the weekend with Marcelo replacing Fabio Coentrao at left-back. Jupp Heynckes recalled eight first-team players to the starting XI who were rested for their 2-1 win over Werder Bremen last Saturday.
Real Madrid came bursting out of the blocks and after Sami Khedira failed to beat Neuer from Angel Di Maria's cutback in the third minute, the hosts were awarded a penalty when the Argentine's thunderous volley hit David Alaba's arm inside the area three minutes later.
Ronaldo stepped up to take the spot kick and coolly slotted it into the bottom-right corner, sending Neuer the wrong way.
Bayern was unfazed and had two great opportunities to restore parity on the night. Firstly, Robben failed to tuck Alaba's cross away from inside the six-yard box and then Khedira stopped Franck Ribery from tapping in off of a rebound from Mario Gomez's 20-yard strike with just 12 minutes played.
With the Bernabeu rocking, Los Blancos showed just how deadly they can be. In the 14th minute a deflected pass fell to Mesut Ozil and he had enough time to pick out an unmarked Ronaldo on the edge of the box. The Portuguese was clinical and he slid the ball past the keeper and in at his near post.
Bayern was seeing plenty of the ball and continued to look going dangerous as Madrid relied on the counterattack and it was offered a chance to level the tie in the 27th minute.
Pepe recklessly dragged Gomez to the ground inside the area and the referee pointed to the spot. Robben took on the responsibility and exorcised exercisedhis Bernabeu demons despite Iker Casillas' best efforts to keep his penalty out.
The unrelenting action continued as shortly after the hour mark Karim Benzema almost curled a majestic effort past Neuer and Casillas was forced into saves from both Gomez and Robben before the break.
The momentum continued early in the second half as Gomez nodded just wide in the 48th minute and Benzema pulled a sprawling save from Neuer eight minutes later.
It soon fizzled out with the game was so delicately poised as neither side dared commit too many men forward, making for a second period that starkly contrasted the first.
Chances were at a premium and the only clear-cut opportunity came in the 86th minute. Robben's pass found Gomez in space in the area but rather than shoot first time, he opted to control the ball which allowed white shirts to get back and swarm over him and the chance went begging.
It ensured the game would go to extra time and after nine minutes of the first period Pepe fed Ronaldo at the top of the box but the former Manchester United man failed to pull the trigger and test Neuer in the only chance of the half.
Alaba netted the opening penalty but Ronaldo failed to match the Austrian as Neuer got a strong hand to the ball. Gomez then converted Bayern's second and then Neuer saved Madrid's with an almost identical spot kick from Kaka.
Los Blancos pulled one back as Kroos and Phillip Lahm missed while Xabi Alonso scored but Ramos failed to draw level as he skied it from 12 yards.
That offered Schweinsteiger the chance to put Jupp Heynckes side into the final and deny Jose Mourinho the chance to face his former club, and he did so, dispatching the penalty with ease.
Bayern can now become the first team to win the Champions League at its home ground when it faces Chelsea in the final next month.