The right-back, 33, has signed a two-year contract with the Rio de Janeiro-based club.
He began his professional career with Brazilian side Coritiba before joining Schalke in 2005 and spending five years in Gelsenkirchen.
Flamengo announced the signing on their website, stating Rafinha would have his presentation at the club on June 24.
His first-team opportunities were limited with Bayern last season, leading to his departure after their domestic double triumph.
He was joined by veteran wingers Arjen Robben and Franck Ribery in bidding farewell to Bayern at the end of the campaign.
Estamos chegando!!! pic.twitter.com/PTpMCX5Pc4— Rafinha Official (@R13_official) June 10, 2019
The departure of three long-serving figures at the Allianz Arena proved to be an emotional occasion for all concerned.
Rafinha said of severing ties with the German giants: "The eight years have been wonderful, I've had some great moments here.
"The treble in 2013 was special. All things come to an end eventually.
"We are together every day and know each other so well - we are a family. The friendship we all have is the greatest thing."