The midfielder signed for Liverpool last week and impressed on his debut in the win over Chelsea and Reds boss Klopp is delighted to have a player of his ability in his squad.
He told Sky Sports News: "Thiago is obviously a very good football player. You saw it [against Chelsea].
"Some things are natural for him that are not natural for other players, but we won the league and we won the Champions League without Thiago.
"He won it with Bayern, so obviously it is a good fit I would say, but we now have to get used to each other."
Klopp added: "There are very special things [he has that separates him from others] in world football. His vision is exceptional, pair that with pretty good technical skills, and a nice passing ability and these kind of things, and you become a really interesting package.
"That's what Thiago is. On top of that as a guy, he couldn't be better. It's incredible, when you give him a ball, he is still a kid.
"And when you take the ball away he is a really mature and experienced football person, who is interested in a lot of things, tactics and all these kind of things. He wants to learn which is very important."
Klopp added that the Premier League champions are looking to try and trim their squad before the transfer window shuts next month as it currently consists of more than 30 players.
The German said: "You cannot or you should not have a 30-player squad. That makes no sense we don't have enough games for that."