Two late goals in regulation and a missed Robben penalty in extra time sent the final to penalties, where Didier Drogba struck the decisive kick from 12 yards out
Bayern set up camp in the Chelsea half for the majority of the match, but was extremely wasteful in front of goal, passing up a number of opportunities that allowed Roberto Di Matteo's men to stay in the contest.
Thomas Muller looked to have finally broken their resistance when he scored in the 83rd minute, but Didier Drogba brought the Blues back from the dead with a powerful header two minutes from time to send the final into extra time.
Arjen Robben saw a soft penalty saved by Petr Cech in the 95th minute, but there was no winner in the additional 30 minutes as the match moved into a penalty shootout.
Drogba struck the winning attempt from the spot to send the Londoners to their first-ever Champions League crown, and finally put the demons of their 2008 failure in Moscow to rest.
Resplendent in their adidas kits, both outfits were forced to reshuffle their XIs due to suspensions, but the biggest surprise came from Di Matteo, who unexpectedly began with 22-year-old left-back Ryan Bertrand in midfield for his first ever Champions League appearance.
The changes seemed to affect Chelsea more than Bayern, with the German side looking far more comfortable during a commanding, but profligate first-half showing.
Bastian Schweinsteiger was denied by a block from Cahill, just before Toni Kroos flashed wide from 18 yards out, all in the first five minutes.
Chelsea was nowhere to be seen in the attacking third, and remained penned back in its own half as Bayern just kept coming.
Mario Gomez nodded a Franck Ribery cross just over, and Cech did just enough to tip a tricky Robben effort onto the woodwork.
It took Chelsea 34 minutes to register its first sight on goal after a clumsy challenge by Jerome Boateng on Cahill on the edge of the area, but Juan Mata sent the set-piece clean over the bar.
That sparked a flurry of chances, with Salomon Kalou tested Manuel Neuer at his near post just after Ribery and Muller both missed from good positions.
The Bayern pair embarrassed themselves with poor control attacking a loose ball in close, but Gomez was guilty of an even greater gaffe two minutes before half time, blasting miles over after twisting away from Cahill deep inside the box.
Drogba almost surprised Neuer with an outlandish strike from all of 40 yards shortly after the restart, but the chance proved to be something of an aberration as Bayern continued to threaten.
Kroos and Robben were both denied by fantastic last-ditch challenges from David Luiz and Ashley Cole, before Ribery saw a goal correctly disallowed for offside.
With 15 minutes to go, Diego Contento was forced to mirror the efforts of the Chelsea rearguard, sliding in to intercept a dangerous Drogba centre from the left.
But Bayern was its own worst enemy, and when Muller spurned a pair of chances with 10 minutes remaining, it looked like its profligacy would finally tell.
However, Muller would come good in the 83rd minute, arriving at the back post to nod in a teasing cross from Toni Kroos to finally send Bayern into the lead.
It looked like the end of the road for Chelsea, but incredibly, the club found itself level with two minutes to go, as Mata’s corner was met emphatically by the head of Drogba to send the tie into an additional 30 minutes.
The Ivorian almost went from hero to villain four minutes into extra-time, as he tripped up Ribery in the area to give Bayern a penalty.
Robben steadied himself from 12 yards, but saw his weak spot kick smothered by Cech, echoing his costly miss against Borussia Dortmund in the Bundesliga.
Daniel Van Buyten came within inches of turning in a cross from Ivica Olic, before Bayern was blocked for the umpteenth time, Cahill throwing himself in front of Gomez from in close.
But no winner was forthcoming, meaning that penalties were required to determine the destiny of the trophy.
In the shootout, Didier Drogba struck the winner from 12 yards out, after Cech saved from Olic and Schweinsteiger to send the 2011-12 Champions League trophy to Stamford Bridge.