Bayern will pay a loan fee of 8.5 million euros ($9.44 million) and pay his wages. They have the option of making the deal permanent for a fee of 120 million euros.
The Brazil international has been linked with a move away from Catalonia throughout the summer after failing to establish himself in the first team and Bayern have pounced as they look to replace the departed duo Arjen Robben and Franck Ribery.
- Dybala set for €80m PSG talks - Paper Round
- Spurs boss Pochettino wants Premier League to extend transfer deadline
Ronaldo and Buffon star as Juventus beat Sassuolo
"FC Barcelona and Bayern Munich have reached an agreement for the loan of the player Philippe Coutinho to the German club for the 2019/20 season," Barcelona said in a statement.
"Barcelona would like to thank to publicly thank Philippe Coutinho for his commitment and dedication wishes him all the best in this new stage of his career."
Coutinho will wear the number 10 shirt previously worn by Dutchman Arjen Robben, who retired at the end of last season.
"We've been working on bringing in Philippe Coutinho for quite some time and we're very happy that we've been able to complete this transfer," Bayern CEO Karl-Heinz Rummenigge said.
"Our thanks go to FC Barcelona for agreeing to the transfer. With his creativity and outstanding skills, Philippe is a player who will immediately strengthen our attack."
Bayern, who drew their first league game 2-2 with Hertha Berlin last weekend, play away at Schalke on Saturday.
Additional reporting from Reuters
Robben dreaming of Holland spot at Euro 2020
Kane to Man Utd less likely, Bayern confident on Haaland – Paper Round