The unlikely storyline of an English team beating a German team on penalties in a high profile match provided a fitting end to a dramatic night, as Chelsea became Europe's champion club for the first time.
The often theatrical 34yearold Drogba, playing possibly his last game for the club as his Chelsea contract expires next month, was at the heart of the show.
Drogba sent goalkeeper Manuel Neuer the wrong way on the final kick of the shootout in front of massed Bayern fans in their home Allianz Arena.
Bayern's Bastian Schweinsteiger missed the previous penalty, hitting the goalpost.
"It was written, I think, a long time ago," Drogba said to British broadcaster, ITV, of Chelsea's turnaround since its turmoil in March. "This team is amazing. They never give up until the end."
The shootout was needed after Chelsea goalkeeper Petr Cech saved Arjen Robben's spotkick early in extra time.
It was awarded for a foul by Drogba, who earned Chelsea an unlikely reprieve.
After 83 minutes of Bayern domination, Thomas Mueller broke dogged Chelsea resistance with a header past the outstanding Cech.
Chelsea's first Champions League title came four years after losing in a shootout to Manchester United.
Drogba succeeded where his captain John Terry, who was suspended for Saturday's finale, failed in missing the fifth penalty in Moscow four years ago which would have given the club's Russian owner, Roman Abramavich, the Champions League title he has craved.
Abramovich must now make a fascinating decision on the future of interim coach Roberto di Matteo, who took over from the fired Andre Villas-Boas after a last16, firstleg defeat to Napoli, and inspired a team which then appeared sulky and fading.
Victory also sealed Chelsea's last remaining route into next season's competition which is crucial to its elite status and finances.
Everything seemed stacked against Chelsea when Bayern won the toss to send the shootout to the home, south end of its stadium.
After Bayern captain Philipp Lahm scored first, Juan Mata has his kick saved by Neuer.
Cech then saved Ivica Olic's fourth penalty for Bayern to put the otherwise excellent Schweinsteiger in the spotlight.
He struck the post to Cech's left and covered his face with his shirt.
Drogba stepped up and sealed victory and awaited the adulation of his onrushing teammates.
"He's a hero. Without him we're not here," said Lampard, who scored with Chelsea's third penalty. "I'd love him to stay. What he did tonight he's been doing all his career."
With seven starters from the two teams suspended, Bayern settled quickly against a visiting team set up to absorb pressure.
The Germans' tempo was often dictated by Schweinsteiger, who excelled after collecting a needless yellow card in the second minute for handball.
The second half resumed with the same pattern, and Cole's outstanding defending denied Robben.
Drogba's taste for the dramatic flared up in the third minute of extra time, as he clipped Ribery's heels in the penalty area.
Referee Pedro Proenca's decision to point to the spot seemed to stun the Bayern fans, and their anxiety was well founded.
Robben fired low to Cech's left, and the Czech 'keeper blocked with his arm and body, then reached across to collect the loose ball.
Bayern came agonizingly close in the 108th, when substitute Olic slipped the ball across the goalmouth but teammate Daniel van Buyten failed to anticipate the simple tap-in.
Bayern Munich: Manuel Neuer, Philipp Lahm, Anatoliy Tymoshchuk, Jerome Boateng, Diego Contento, Bastian Schweinsteiger, Toni Kroos, Arjen Robben, Thomas Mueller (Daniel van Buyten, 87), Franck Ribery (Ivica Olic, 97), Mario Gomez.
Chelsea: Petr Cech, Jose Bosingwa, David Luiz, Gary Cahill, Ashley Cole, John Obi Mikel, Frank Lampard, Salomon Kalou (Fernando Torres, 84), Juan Mata, Ryan Bertrand (Florent Malouda, 73), Didier Drogba-AP.Post published in: Football