The Spanish goalkeeper, who spent last season on loan at Napoli, has signed a three-year deal with the German champions.
He is expected to be the back-up to Manuel Neuer at the Allianz Arena next season.
On the signing of Reina, Bayern chairman Karl-Heinz Rummenigge said on the club's official website: "It reflects what we were looking for. We wanted a goalkeeper who is experienced and established and also has certain footballing qualities."
Reina wrote an open letter paying tribute to Liverpool staff and fans on his official website.
"I have been extremely fortunate to spend so many years at what I consider to be one of the greatest clubs in world football," he said.
"It has been an honour and a privilege. The memories I have of Anfield, my team-mates, the supporters and the people of Liverpool will stay with me forever. I am disappointed that I am leaving, but only in the sense that I enjoyed being at the club so much and it is always difficult to say goodbye to something that is special to you."
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