The Germany international will be one of seven national-team players familiar to former Germany coach Jurgen Klinsmann, who takes over at the Bavarians in the summer.
The 27-year-old will move on a free transfer with Bremen general manager Klaus Allofs admitting his club could not compete financially with Bayern, saying: "We made an offer to Tim last year, but he did not want to negotiate. When a player from the Germany set-up becomes available, then you have got to expect these developments."
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