Petersen has joined Werder Bremen on a one-year loan deal.
The 23-year-old has also extended his contract with Bayern Munich until the summer of 2015.
“Nils is a great talent, and we want to get him some match practice – which he will be able to do with Bremen,” Bayern Munich general manager Christian Nerlinger told the club’s official website.
“The fact that we have also extended his contract is a sign of how much we value him. We want him to have a successful future in the Bundesliga and Bayern.”
Werder Bremen coach Thomas Schaaf said: “He is a centre forward who has demonstrated his goal-scoring talent. We are delighted that he is joining us. We are sure that he’ll have all the right conditions to develop here.
Bremen sporting director Klaus Allofs added: “We have waited a long time for this transfer, and are pleased that it’s now signed and sealed.”