Antonio Conte has won the race for the Spain striker, who will become a Bianconeri player on July 1 after seeing out the remainder of his contract with Athletic Bilbao
The 27-year-old has been frozen out of the picture at the Basque club after rejecting a new contract that would have seen his salary rise to €4.8 million [£4m] a year.
Llorente will earn less at Juventus, €4.5m [£3.8m] per season, but had his heart set on Italy and has now agreed a four-year contract.
The Serie A holders attempted to sign Llorente in the summer but baulked at the €36m [£30.2m] buy-out clause written into the player's contract.
Llorente has been free to speak to overseas clubs about a summer transfer since January 1.
The deal was to be announced by the Turin club on Wednesday, but was held back so as not to overshadow the new two-year contract extension agreed by captain Gianluigi Buffon.