The 21-year-old will join the German champions at the end of the season along with team-mate Sebastian Rudy, Bayern having announced the deal in January.
Sule had been on Antonio Conte’s shortlist as the Chelsea manager looked to revamp his defence and the German international revealed an offer had come in from Stamford Bridge at the same time as he was being courted by Bayern.
“Both offers came almost simultaneously,” he told TZ.
“Of course it was huge for me that the Premier League leaders showed interest in me, but it felt better to stay in the Bundesliga.
“And Bayern are the top address – there is nothing greater in the world.”
At both international and club level Sule will spend next season competing with central defensive pair Jerome Boateng and Mats Hummels for a starting role.
And Sule is eager to learn from two of the best defenders in world football as he looks to establish himself as the Bayern centre-back of the future.
“I think I can learn a lot from both,” he said. “If I look at myself every day, compared to Mats and Jerome, I can bring myself to a completely new level.
“They are much more experienced than me and unbelievable on the ball. When you see how Mats builds the game, that's madness. With Jerome it's his dynamism, his athleticism and his one-on-one duels.”