The France winger, now 20, joined Bayern on a two-year loan deal in 2015 and they had until the end of April this year to make the deal permanent for 21m euros (£17.75m).
Coman has scored eight goals in 58 games for Bayern.
The former Paris St-Germain player's Bayern contract will run until 2020.
"Kingsley Coman is an important building block for the future of our team, so we decided to take the option," said Bayern chief executive Karl-Heinz Rummenigge.
"Kingsley is a hopeful player with great potential. We are convinced he will help us in the coming years."
Find all the latest football transfers on our dedicated page.
Bayern Munich will activate the clause to make Kingsley Coman's transfer from Juventus permanent at the end of the season.