The 17-year-old has signed a five-year contract at the Allianz Arena.
Tel came through Rennes' youth ranks and made just 10 appearances for the first team, failing to score but comes with a big reputation.
Tel recently captained the France u-17 side European u-17 championship glory.
He becomes Bayern Munich's fifth signing of the summer.
The Bavarians have lost Robert Lewandowski to Barcelona but have also brought in Sadio Mane, Ryan Gravenberch, Noussair Mazraoui and Matthijs De Ligt.
"FC Bayern are one of the best teams in the world. I'm very much looking forward to this great challenge and I will give my all for this club," Tel said after the signing ceremony.
"I've been very impressed with the discussions with Hasan Salihamidzic and the FC Bayern management, and I quickly realized I definitely wanted to come to Munich."
Bayern Munich's sporting director Hasan Salihamidzic added: "Mathys Tel is one of the biggest talents in Europe, a very quick, technically strong and versatile striker. He won the European Championships with the France U17s this year as captain of the team. We've been watching him for a long time and we were able to convince him to take his next important steps in Munich with us now. We are proud of that, as there were a lot of clubs who wanted to sign him."
"The development of such an exceptional young player is an exciting project for us all. Of course, Mathys needs time, he needs minutes on the pitch and rhythm. We are all convinced he has a great career in front of him and that he will help our team."
