"He is a player with huge potential," Bayern CEO Karl-Heinz Rummenigge said. "We're convinced that he will be of great help to us in the coming years.
"He is a very young player who already plays regularly for the French national team and who has gathered experience at the European Championship."
Coman, a former Paris St Germain player, has scored eight goals in 58 games for Bayern.
Rummenigge also heaped praise on 26-year-old Thiago, who signed a two-year extension that will keep him in Munich until 2021 and has arguably played his best football at Bayern this season.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
"Thiago is one of the best and most sought after midfielders in Europe," Rummenigge said. "We are happy to have tied him to the club on a long-term basis."
The Spain international is the latest stalwart to sign up to 2021 following - among others - Jerome Boateng, Mats Hummels, Thomas Mueller, Robert Lewandowski and keeper Manuel Neuer as Bayern look to retain key players.
(Reporting by Hardik Vyas in Bengaluru; Editing by Amlan Chakraborty and John Stonestreet)
