Villas-Boas told CNN World Sport that Guardiola will become "one of the greatest managers in football".
He said: "I'm so surprised that I asked my media advisor from Tottenham if it was true. Obviously its a big, big club, one of the biggest clubs in the world, in a league where we didn't maybe expect Guardiola to be in.
"Obviously, there's a great respect from all managers towards Jupp Heynckes and what he has achieved in his career. Guardiola is obviously going to become one of the greatest managers in football. He's won I think 14 trophies and he's had such an amazing career.
"I think in Bayern he will find the right set-up to continue, not only to promote his message of football, which is immense, the way he believes in this game and the way he has changed the nature of the game people appreciate it and I think the example that he is.
"As a person, as a leader, through his professional career and through his coaching career too."