The Bianconeri confirmed the signing of the striker on Wednesday after he was pictured holding aloft the club's home shirt, emblazoned with the number 10, with the two clubs having agreed an €11.8 million fee for the player on Tuesday.
The 29-year-old - whose contract was set to expire at the Etihad in the summer of 2014 - had long been rumoured to be the Rossoneri's main transfer target this summer.
But the revelation from Milan chief Adriano Galliani that the club will have to sell before they can buy this summer, left Juve clear to secure his signature.
"I'm really happy to be here at Juve," Tevez told Sky Sport Italia.
"It's a really big satisfaction for me. I will tell the rest in the press conference - but Juventus wanted me more than Milan."
Tevez joined City from rivals Manchester United in 2009 and endured a controversy-ridden time at the club, including a five-month absence for refusing to come on as a substitute away to Bayern Munich in the Champions League.
He scored 17 goals in 47 appearances last season and ended the campaign as City's joint-top goalscorer with Sergio Aguero.