Bayern beat tomorrow's Champions League opponents Manchester United to Kane's signing as he was leaving Tottenham.
Tuchel said, "It's a massive thing. We took the skipper out of England and the Premier League, it's huge and we're very happy.
"Anyone who is looking for a number nine would be happy to have Harry [Kane] because he makes you better and gives you everything.
"He can drop deep to a number 10 position and use the speed of players around him, he can arrive in the box, has excellent finishing and is a great penalty taker.
"I don't know what's happening at other clubs but I'm glad he took the decision to come to us.
"He will always be a difference-maker in any game, not only the big games and not only by goals but he also gives us personality.
"In time he will make players around him better and will learn how to make them shine. He will assist and not only score. He will be the difference and he is already the difference.
"He is very important and that's why we relied heavily on this transfer and I'm 100% convinced he will prove us right."
The German added: "It's good that we all speak English so there is no problem in communication.
"Harry [Kane] has been doing this for almost a decade, carrying Tottenham on his shoulders and he never hid from pressure. He also does it for the England national team and does it in his own kind, humble and friendly style.
"There isn't just one leadership style or one leader you have imitate to lead a group of football players. He does it in his way and isn't shy to do it here. He hasn't become a new person, he's the same guy and that's what we wanted. He is calm under pressure."