Sturaro has agreed a five-year contract with the defending Serie A champions after the two clubs agreed a €5.5 million transfer.
With competition for places high at Juventus Stadium, the club have opted to leave Sturaro with Genoa for the 2014-15 campaign, enabling him to continue his development before linking up with Antonio Conte's squad.
A statement from Juve read: "Juventus announces that the agreement with Genoa for the definitive acquisition of the registration rights of Stefano Sturaro has been finalised.
"The contract includes the payment by Juventus of €5.5m over three years.
"The purchase value may increase by a further €3.5m depending on performances during the contract from 2015-16."
Sturaro made 16 appearances for Genoa last term, having risen through the youth system at Stadio Luigi Ferraris.
The 21-year-old had a loan spell at Serie B outfit Modena in the previous campaign.
