Drogba, who had equalised for Chelsea two minutes from the end of normal time, rolled the winning kick past Manuel Neuer as the visitors edged the shootout 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 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.
Image: Chelsea team celebrate with the trophy at the end of the Champions League final soccer match between Bayern Munich and Chelsea in Munich, Germany Saturday May 19, 2012. Didier Drogba scored the decisive penalty in the shootout as Chelsea beat Bayern Munich to win the Champions League final after a dramatic 1-1 draw on Saturday.