The Peru striker, who made 174 appearances and scored 71 goals in his first spell with Bayern between 2001 and 2007 before joining Chelsea, has signed a one-year contract with the Bavarians after his contract with Bremen expired this summer.
"We are pleased to have been able to sign Claudio Pizarro, an internationally experienced and very dangerous striker," said Bayern's director of sport Christian Nerlinger on his club's website.
Since returning to Bremen in 2008, Pizarro has become the Bundesliga's all-time top foreign goalscorer with a total of 160 goals in 333 games.
This experience made him the ideal candidate to replace Ivica Olic, who has left Bayern to join Wolfsburg, and put pressure on Bayern's number one striker Mario Gomez next season.
Pizarro underwent a medical in the Bavarian city last week and put pen to paper on a contract last night in Madrid, when he met Nerlinger at the Spanish Copa del Rey final between Barcelona and Athletic Bilbao.
He is Bayern's fourth new signing this summer, joining Xherdan Shakiri from Basel, Tom Starke from Hoffenheim and Dante from Borussia Monchengladbach.