The 27-year-old has signed a four-year deal and cost Juventus 15 million euros, to be payable over three years.
He is the fifth major signing made by Juve this close season following the arrival of midfielders Andrea Pirlo from AC Milan and Arturo Vidal from Bayer Leverkusen as well as full-backs Stephan Lichsteiner (Lazio) and Reto Ziegler (Sampdoria).
Former AC Milan forward and current Montenegro Football Federation president Dejan Savicevic said Juve had done well to procure Vucinic's services.
"Juventus have done well to take Vucinic, he's a great signing," Savicevic told Tuttosport.
"With him, the black and whites can get back to winning ways. He's a great player, one of the best five or six strikers in the world.
"And now that he's matured this transfer will allow him to take a definite step up in quality.
"He could have gone to Chelsea or Manchester United because Mirko has the ability to play in big clubs and he deserves it.
"Football goes in cycles, as happened with Milan. After some tough seasons Juventus should get back to being one of the best."