The Spain international, who spent last season on loan at Napoli, will join the German champions as back-up for number-one keeper Manuel Neuer if he passes a medical.
A statement on the Bayern website confirmed terms have been agreed with both Reina and Liverpool.
And chairman Karl-Heinz Rummenigge said: "The player will come to Munich in the next few days for a medical examination and to sign his contract.
"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."
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.
Meanwhile, Bayern boss Pep Guardiola has dismissed reports linking central defender Jerome Boateng with Barcelona.