Tolisso comes from French Ligue 1 club Olympique Lyonnais, which he joined as a teenager. He became the club's biggest transfer, beating the previous mark of 40 million spent on Javi Martinez in 2012.
The French club said in a statement it was also its own biggest transfer to date and could bring in another 6 million euros based on incentives included the deal with Bayern.
"I had a wonderful time at Olympique for which I am thankful. Now I look forward to playing at one of the best clubs in Europe," the player said in a Bayern statement.
"I have set big goals for myself at Bayern. Today is a big day for us."
Bayern have won the German league a record five consecutive times but have not made it past the semi-finals in the Champions League since last winning the title in 2013.
"We are delighted to have won over this young and highly interesting player despite international competition," Bayern CEO Karl-Heinz Rummenigge said. "Corentin Tolisso was top of the midfield wishlist for our coach Carlo Ancelotti."
(Reporting by Karolos Grohmann; Editing by Alison Williams)
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