The Austrian leaves Leipzig after six years with the club, where he won the German Cup twice, including in his last game for the team. The 26-year-old has signed a contract with Bayern until 2027.
"It's a dream come true for me. FC Bayern is one of the biggest clubs in the world," Laimer said in a statement. "I will give everything for the club and the fans. FC Bayern always has the highest goals -- just like me. I'm in the right place here."
Laimer is the first Bayern signing since the club fired Oliver Kahn as chief executive and Hasan Salihamidzic as sporting director last month. However, arrangements to sign Laimer were widely reported to have been made long before Kahn and Salihamidzic left.
Laimer scored against Bayern for Leipzig in a 3-1 win for his old club last month, leaving Bayern in second place behind Borussia Dortmund in the standings ahead of the last day of fixtures. However, Bayern beat Cologne to win the title on goal difference after Dortmund drew with Mainz.