The former Liverpool striker completed his move to Bayern yesterday.
Nagelsmann said: "What changes with his transfer? You can't say 100 percent yet, we'll also have to see what else happens on the transfer market. But Sadio is a player who can play four, five positions without problems and can even change during the game.
"We are Bayern Munich. We always have the opportunity to bid for big stars. Sometimes we reach financial limits, especially when the boys play in England. With Sadio it was different because he is very interested in our project, in the club and his teammates."
"He's a world star that we brought to Munich. We are all happy and proud. He is not only a great player, he has a monstrous mentality. We need him to win as many titles as possible."