The Spain midfielder has seen a fee of €30m agreed between the two clubs in the last 48 hours.
This morning, Thiago said: "My decision has been a sports decision. As a player I want to take on new challenges and continue to evolve.
"Bayern will always remain my home."
He continued: "I am proud to have arrived as a young man full of dreams and to leave now full of the club, its history and its culture. Here I have learned to love a tradition that I now say goodbye to but that I will never forget."