The center back has an expiring contract with his current club, and he will sign a deal with the Bavarians until June 2016.
"We are very pleased that such a young and talented Under-21 international has made the decision to join Bayern," chairman Karl-Heinz Rummenigge told Bild.
The 22-year-old had also caught the attention of Borussia Dortmund and Schalke, but he has opted to continue his career at the Allianz Arena instead. Kirchhoff came through the ranks of the Eintracht Frankfurt youth academy, before joining Mainz in 2007.
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