The Germany Under-21 defender has attracted the interest of several Bundesliga sides, but is expected to continue his career at the Bavarian giants for at least three years
The centre-back has an expiring contract with his current club, and 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 has opted to continue his career at the Allianz Arena instead.
"Kirchhoff is a rough diamond. I am very happy that he comes to Bayern and has opted to accept the challenge," sporting director Matthias Sammer added.
Kirchhoff came through the ranks of the Eintracht Frankfurt youth academy, before joining Mainz in 2007.