Vidal, 24, was targeted by Bayern Munich but has decided to continue his development in Italy after a €12 million fee was agreed.
"I'm happy, it's a big and important step for my career at one of the biggest clubs in Europe," Vidal told reporters at Santiago airport. "I'm very content about this new opportunity that I'm being given. It's a new team which is being built with the aim of being champions and qualifying for international competitions.
"My experience in Germany will be useful to me in Italy, because tactically it's a similar kind of football."
Vidal spent four seasons at Leverkusen and has starred for Chile, helping them reach the second round at last year's World Cup.
Juventus, despite the fact they won't be involved in European competition this season, have spent €37 million to make four players - Alessandro Matri, Fabio Quagliarella, Simone Pepe and Marco Motta - permanent signings, while they have also sealed moves for Andrea Pirlo, Stephan Lichtsteiner and Reto Ziegler.