Tolisso, 22, joined the Lyon set-up in 2007, aged 13, and came through the club's highly-rated youth system before making his Ligue 1 debut in the 2013/14 season and playing every game of the following campaign. He made a total of 116 top-flight appearances over four seasons, scoring 21 goals.
The midfielder, who becomes the third Frenchman in the current Bayern squad, made 47 overall appearances last season, scoring 14 goals and claiming seven assists.
"I had a wonderful time with Lyon, for which I am very grateful," Tolisso said. "Now I'm looking forward to playing at one of the best clubs in Europe. I have set myself high goals at Bayern Munich. Today is a great day for me."
"We are very happy that we were able to sign this young and interesting player, despite strong competition from abroad," said club CEO Karl-Heinz Rummenigge. "Corentin Tolisso was the dream player for our head coach, Carlo Ancelotti, in midfield."
Having made his France debut in a 2-0 friendly loss to Spain in March, Tolisso now faces the daunting task of filling the sizeable gap left by the retiring Xabi Alonso in the heart of the Bayern midfield.