The Spain international goalkeeper, who spent last season on loan at Napoli, has signed a three-year deal with the German champions.
He will provide back-up to Germany international Manuel Neuer at the Allianz Arena.
Reina, who will turn 32 at the end of August, was a regular at Liverpool for eight seasons before Brendan Rodgers signed Belgium's Simon Mignolet from Sunderland last summer.
Rodgers has Brad Jones as cover and sanctioned Reina's temporary move to Napoli last season.
Napoli boss Rafa Benitez was known to be interested in signing Reina on a permanent deal, but the Serie A side 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.
Bayern Munich chairman Karl-Heinz Rummenigge revealed Reina’s keenness to join the Bundesliga side earlier in the week.
Rummenigge said: "He was eager to come to Bayern Munich. He wanted to embark on this adventure even though he knows that, in Manuel Neuer, he has a keeper in front of him who, if nothing changes, will always remain the number one."
And after completing the deal, he added: "It reflects what we were looking for. We wanted a goalkeeper who is experienced and established and also has certain footballing qualities."
Reina will be officially presented to the club's fans at an open day at the Allianz Arena on Saturday.
Following his departure, 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."