The striker had reportedly been targeted by Manchester United, Blackburn and Tottenham but the Montenegro international has opted to stay in Serie A.
The 27-year-old underwent a medical at Juventus on Monday before signing a four-year deal with the Turin club.
"Juventus Football Club announces that the agreement with AS Roma for the definitive acquisition of the registration rights of the player Mirko Vucinic has been finalised," read an official Juventus statement.
"The contract envisages the payment by Juventus of €15m (£3m) in three years.
"Juventus and the player have signed a four-year contract of agreement."
Vucinic had spent five years at Roma, where he scored 46 goals in 147 appearances.