The 31-year-old watched on the sidelines as the Blues ran out 2-1 winners against Club America in Las Vegas.
His £33million move from Napoli is a Premier League record fee for an over-30 player, but Tuchel has backed the Senegal international to remain at the top level for years to come.
"That's what we believe and that's what he is here for," Tuchel said at the Allegiant Stadium. "There were always rumours about him leaving Napoli and it was always super difficult – and in the end impossible – to get him because he was a key player.
"It's nice he takes the challenge right now and we have Thiago Silva, who is even older and super experienced and still at the peak of his game. We hope Kalidou can do the same and play for many years for us.
"He is totally fit and ready for the challenge and he needs to be because we need him in top shape."
The Blues squad has also been bolstered by Raheem Sterling, who joined in a £47.5m move from Manchester City, while there are talks ongoing to sign Paris Saint-Germain's Presnel Kimpembe and Sevilla's Jules Kounde.
There are also a number of returnees looking to impress, namely Conor Gallagher. And Tuchel was impressed by the England international against Club America.
"Conor trains at a really high level and you can clearly see it was the right decision to let him go on loan," he added.
"He made a huge step in his development at Crystal Palace and became an England player. We can see this clearly in training, it was a very good start and a good match for him.
"Now for him, he must get used to our principles of the game, to understand when to move and when not to move, and his work rate is outstanding and he has such a big heart. He can be a big asset for us."