Barcelona say the German side will pay 8.5m euros (£7.78m) to take the Brazilian, 27, on loan while the option to buy stands at 120m euros (£109.84m).
Bayern will also pay Coutinho’s wages for the duration of the loan spell.
“For me, this change represents a new challenge in a new country at one of the best clubs in Europe,” he said.
“I am really looking forward to this. I have big goals, like Bayern, and I’m sure I can do it with my new team-mates. “
Bayern chief executive Karl-Heinz Rummenigge added: “We have been working with Philippe Coutinho for some time and are very happy that we were able to realise this transfer now.
“Our thanks to FC Barcelona for agreeing to this transfer. In Philippe, a player comes to FC Bayern who will strengthen our offensive with his creativity and excellent technique.”
Despite scoring 21 goals in 76 appearances for the Spanish giants, he has fallen short of expectations and had been linked with several clubs this summer.
It is believed he was included as part of a bid by Barcelona to re-sign Neymar from Paris St-Germain, the Spanish club reportedly willing to offer 100m euros (£92.4m) plus Coutinho for the forward.