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 served as Liverpool's number one for eight seasons following his signing from Villarreal in 2005, but the arrival of Simon Mignolet last summer saw him reunited with former Reds boss Rafael Benitez in Italy.
Benitez was known to be interested in signing the Spain international on a permanent deal, but Napoli refused to meet the £3.95million release clause in his contract and Reina travelled to the United States for Liverpool's pre-season tour following the World Cup.
He will now make a fresh start in Germany, although the 31-year-old will have his work cut out to dislodge Neuer, perhaps the best keeper in the world at the moment, from the number one spot.
Reina came through the ranks at Barcelona, but could never fully establish himself at the Nou Camp and moved to the Yellow Submarine in 2002, spending three seasons with the club before his move to the Premier League.
While at Anfield, Reina won the FA Cup, League Cup and European Super Cup and added the Coppa Italia to his list of medals in Naples last season.
Reina will be officially presented to the club's fans at an open day at the Allianz Arena on Saturday.
Reina should be the last new face to arrive at the record German champions this summer with Rummenigge saying "at most" one or two young players may be loaned out.
He added: "That's because we would like them to get more match practice."
- Sports & Recreation
- Manuel Neuer
- Karl-Heinz Rummenigge