Can left the Reds on a free transfer at the end of his contract this summer after failing to agree a new deal with the club despite lengthy negotiations.
Rumours of a fallout with Klopp over his position in the team have begun circulating following his exit, but the Germany international has played down any rift.
"I had problems with Klopp? No, I had no problems with Klopp. I had a very good relationship with him. At the end he wished me all the best here. I never had problems with Klopp," Can told reporters at his official unveiling.
"I know the mentality of this club well, there's a winning mentality and it's my mentality, I'm here to win titles. I decided to come to Juventus because I think the project here is very big. They have very big aims. I want to be part of the project here.
"I am really happy to be here. I know how Juventus play, I watched a lot of the games last season. One of my biggest idols was Zidane who played here too."
Can made 166 appearances for Liverpool during his four seasons at the club, scoring 14 goals.