The Bavarian giants confirmed they had reached an agreement with the Poland international, who has put pen to paper on a five-year deal from July 1, 2014.
A statement on Bayern's Twitter feed said: "£FCBayern have signed Robert Lewandowski (25)! The striker has signed a 5-year contract until 2019."
Chairman Karl-Heinz Rummenigge was delighted with the deal, saying on Bayern's official website: "We are very pleased that this transfer is successful.
"Robert Lewandowski is one of the world's best strikers, he will strengthen the squad of FC Bayern and give us a boost.
"We are very pleased that today, from both sides, a five-year contract was signed until 2019."
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