Didier Drogba, who had equalised for Chelsea two minutes from time, struck the winning kick past Manuel Neuer as the visitors edged the shoot-out 4-3 after Bastian Schweinsteiger's last kick for Bayern had hit the post.
Bayern, playing in their home stadium, laid siege to Chelsea's goal for most of the game and appeared to have won it when Thomas Mueller finally made the breakthrough with an 83rd minute header past Petr Cech.
Within touching distance of lifting the famous trophy for the first time since 2001, Bayern conceded with two minutes remaining when Drogba met a corner with a thumping header to give Neuer no chance.
Bayern, four-times winners, were stunned and extra time could not separate the sides despite Bayern earning a penalty which Arjen Robben saw saved by Cech.
Chelsea lost to Manchester United in the 2008 final on penalties but erased that painful memory as they held their nerve to become London's first European champions.
The match itself was marked by drama rather than excellence.
Both sides were decimated by suspensions and injuries: Chelsea were without John Terry, banned for his semi-final sending off, but they were hit hardest in midfield, lacking the dynamism of Ramires and Raul Meireles and forced to play young left-back Ryan Bertrand in place of Florent Malouda, who had not trained after picking up an injury but made an impact from the bench late on.
Bayern dominated for large swathes of normal time as Chelsea adopted a similar strategy to that which ousted Barcelona in the semi-finals, although they were even less effective on the counter against the Germans.
But, for all their possession and long-range efforts, Cech’s only major save came from a Franck Ribery shot that he tipped on to the post.
Still, Bayern’s late opener – when Mueller escaped the otherwise excellent Ashley Cole to convert a powerful downward header on 82 minutes – was fully deserved. The English side had only mustered one shot on target, when Salomon Kalou forced a routine stop from Neuer, while Bayern had peppered the Blues’ goal with Mario Gomez again falling short in a pressure situation with two poor finishes.
That sparked a late Chelsea rally, one which paid off in style as Drogba met Juan Mata’s corner with a towering, spinning header that powered into the top right corner off Neuer’s hand.
Bayern had already taken off Mueller, attempting to shore things up with returning defender Daniel van Buyten, so for extra-time they introduced Ivica Olic who is leaving the club this summer.
Normal time had been dominated by the hosts, but extra time was fairly even – however the best chances fell to Bayern, none more so than when Drogba needlessly tripped Ribery in an almost identical incident to that which saw the Ivorian concede a penalty in the previous round.
And, just as Lionel Messi fluffed his lines for Barca, so did Robben as Cech’s huge frame kept out his low shot as he dived to the corner.
There was also time for another glaring miss, Olic this time putting wide after Jose Bosingwa went walkabout – not for the first time in an uneasy performance by the right-back, filling in for the banned Branislav Ivanovic.
It all came down to spot-kicks and things started inauspiciously for Chelsea as Neuer dived to his left to repel Mata's effort.
The excellent Philipp Lahm had already netted, as did team-mate Gomez, while Neuer himself stepped up to fire past Cech.
That display of confidence could have knocked the stuffing out of Chelsea but after David Luiz and Frank Lampard had dispatched their penalties with aplomb, Olic was denied by a wonderful one-handed stop by Cech.
Cole had no trouble with his effort, leaving Schweinsteiger and Drogba to take the final kicks. The German beat Cech, but not the post, while Drogba fired home to send the visitors into delirium.
It was quite possibly Drogba’s last act in a Chelsea shirt as his contract is up in the summer and the 33-year-old is expected to take up semi-retirement in a money-spinning foreign league.
Drogba was unable to take a penalty when Chelsea lost the 2008 final after being sent-off and his joy will be heightened by the feeling that the West London side won the trophy against the odds, giving owner Roman Abramovich a dilemma on whether to give interim coach Roberto Di Matteo the job full-time.
For Bayern it is a third second-best finish of the season, having also lost out in the Bundesliga and German Cup to Borussia Dortmund. It is also the third time they have lost a Champions League final, the last occasion being against Manchester United in 1999 when the German side had also led with just minutes of normal time remaining.
That was also the only other occasion when an English side had won both the FA Cup and the European title, a further boost for English football whose last Champions League win was in Moscow four years ago.