Originally on-loan with Bayern from Tottenham, Dier completed the set objectives last week to make the deal permanent.
Bayern have paid 4m as a loan fee, with Dier joining permanently on a free transfer.
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He has signed to 2025.
Dier said: "I'm happy here in Munich, now my future is decided and I can concentrate on playing well for the team and helping it win matches and competitions, even if we are going through a difficult period."