Barcelona said in a statement that Bayern will pay a loan fee of €8.5 million along with Coutinho's wages for the season.
The Brazilian will wear Arjen Robben's old No. 10 shirt for the upcoming campaign.
"For me, this move means a new challenge in a new country with one of the best clubs in Europe," Coutinho said. "I'm very much looking forward to that. Like FC Bayern, I have big ambitions and I'm convinced that I can achieve them together with my new teammates."
Coutinho arrived at Barcelona in January 2018 as Andres Iniesta's successor but didn't live up to the billing over the following year and a half. He alternated as a left winger and wide midfielder in Ernesto Valverde's ever-shifting formation, but never seemed to be a fit.
However, the 27-year-old seemed to regain his confidence at the Copa America in June, helping his country win the South American title for the first time since 2007.
"He's a world-class player with great ability, who we can deploy in a number of positions in our forward line, so the FC Bayern squad has gained even more quality," Bayern sporting director Hasan Salihamidzic added.
At Bayern, Coutinho is more likely to play alongside Thiago Alcantara and Corentin Tolisso in midfield than he is at left wing, where Ivan Perisic, Kingsley Coman, and Alphonso Davies are all available options.