Peru international Pizarro, the Bundesliga's leading all-time foreign scorer, joined the Bavarians, who lost in the Champions League final to Chelsea last week to end their second consecutive season without silverware, after a three-year stint at Werder Bremen.
"We are delighted to have signed a such a dangerous forward who also has so much international experience," said Bayern sports director Christian Nerlinger.
The 33-year-old, who played for Bayern between 2001-07 before joining Chelsea, has scored 160 goals in 333 Bundesliga matches.
