Vidal, 24, told reporters at Santiago airport that he was flying to Italy to finalise the deal.
"I'm happy, it's a big and important step for my career at one of the biggest clubs in Europe," said Vidal, a versatile midfielder who combines tenacity with skill and has spent four seasons at Leverkusen.
"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."
Vidal had also been targeted by Bayern Munich but Leverkusen, who finished second in the Bundesliga last season, did not want to sell him to their close rivals.
"My experience in Germany will be useful to me in Italy, because tactically it's a similar kind of football," said Vidal.
Juventus finished a disappointing seventh in Serie A last season and missed out on European competition.
They have since replaced coach Luigi Delneri with former midfielder Antonio Conte and last month splashed out 37 million euros to make four players - Alessandro Matri, Fabio Quagliarella, Simone Pepe and Marco Motta - permanent signings.
The club has also been linked with Villarreal striker Giuseppe Rossi and Atletico Madrid's Sergio Aguero.
Vidal began his career with Colo Colo and helped Chile reach the semi-finals of the under-20 world championship in 2007. He played in the Chile team which reached the second round at last year's World Cup.
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