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 figure of 34-year-old 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 to win the shootout 4-3 in front of massed Bayern fans in their home Allianz Arena. Bayern's Bastian Schweinsteiger missed the previous penalty.
The shootout was needed after Chelsea goalkeeper Petr Cech saved Arjen Robben's spot-kick early in extra time.
Robben’s kick was awarded for a foul by Drogba, whose 88th-minute header earned an unlikely reprieve.
After 83 minutes of Bayern domination, Thomas Mueller broke dogged Chelsea resistance with a header past 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 the finale, failed in missing the fifth penalty in Moscow four years ago.
The 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 end of its stadium. After Bayern captain Philipp Lahm scored first, Juan Mata saw 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 then sealed the victory and awaited the adulation of his onrushing teammates.
Didier Drogba, Drogba, Bayern Munich, Bayern, Champions League, Bastian Schweinsteiger, Chelsea, Petr Cech, Manuel Neuer, Arjen Robben