The 27-year-old has signed a four-year contract.
Vucinic is Juve's fifth major capture this summer following the arrivals of Andrea Pirlo, Arturo Vidal Stephan Lichsteiner and Reto Ziegler.
Ex-AC Milan forward and current Montenegro Football Federation president Dejan Savicevic believes 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."