The Italian champions have beaten Fenerbahce and Malaga in the race to sign the 34-year-old.
Lucio was tied for one more year to Inter Milan but terminated his contract with the Nerazzurri outfit earlier this week.
A statement from Juventus read: "Today [Wednesday] is the day for Lucio to undergo a medical.
"The Brazilian defender has arrived in Turin this morning [Wednesday] to undergo the appropriate medical examinations at the Sessant Clinic of Fornaca."
Lucio is expected to sign a two-year contract with the Bianconeri outfit.
The South American joined Inter from Bayern Munich in the summer of 2009 and won the scudetto, Serie A and Champions League titles in his first season in Italy.
When asked about Lucio's imminent move to Juve, Inter Milan president Massimo Moratti said on the club's official website, www.inter.it: "These things happen in football. When you rescind a contract, a player is free to go wherever he wants to."