The Spain international, whose deal with Athletic expires at the end of June, will become a Juve player on July 1st.
"The 27-year-old has agreed terms on a four-year deal and will move to Turin when his Athletic Bilbao contract expires at the end of the current season."
In November, Llorente announced his decision to leave the club where he has spent nine seasons since graduating from the academy.
Llorente has made 334 appearances for Athletic, scoring 104 goals in all competitions, with his best return coming during the 2011-12 campaign when his 29 goals helped the Basque outfit to the Copa del Rey and Europa League finals.
His prolific record at San Mames has also earned Llorente international recognition. He has scored seven goals in 21 appearances for Spain and was included in the squads that won the 2010 World Cup and 2012 European Championship.
Llorente has been used sparingly by Athletic coach Marcelo Bielsa since declaring his intention to leave, but his lack of activity has not dissuaded Juve, who currently lead the Serie A table by five points in their bid to retain the title.
Despite their dominance, Bianconeri boss Antonio Conte has struggled to forge an effective strikeforce from a pool of Mirko Vucinic, Fabio Quagliarella, Sebastian Giovinco and Alessandro Matri, with on-loan Arsenal striker Nicklas Bendtner failing to make an impact due to injury.
Today's announcement cools speculation that Juve were prepared to pay Athletic to release Llorente early, with both Didier Drogba of Shanghai Shenhua and Lyon's Lisandro Lopez being targeted as short-term solutions to the club's lack of firepower