The transfer had been a poorly kept secret, but the move is now complete after swift negotiations and a medical in Bavaria.
Diaz will link up with former Premier League star Harry Kane in the Bundesliga and could replace Leroy Sane on the left flank.
The Colombian becomes Bayern's marquee capture of the summer, following the signings of Jonathan Tah and Tom Bischof.
"It means a lot to me to be part of FC Bayern - it’s one of the biggest clubs in the world. I want to help my new team with my style of playing football and my personality," Diaz said.
During his four years with Liverpool, Diaz won one Premier League title, an FA Cup, two EFL Cups and a Community Shield.
"Everybody at Liverpool FC thanks Luis for all of his contributions during his time at the club and wishes him the best for the future," the club posted on social media.
The Reds are now expected to turn their attention to Newcastle's Alexander Isak.