The 34-year-old World Cup winner penned a two-year contract with the Serie A champions after completing a medical.
"Lucio has completed a move to Juventus," a statement on Juve's official website read.
"The Brazilian defender joins the Bianconeri on a free transfer and has signed a two-year contract, keeping him with the club until 30 June 2014."
Juve beat interest from Fenerbahce and Malaga for the veteran who was allowed to leave Inter Milan earlier this week despite still having a year to run on his contract.
Lucio had established himself as one of the best defenders in Italy since his arrival at San Siro, from Bayern Munich, in 2009.
He immediately helped Inter, then under the stewardship of Jose Mourinho, to the scudetto and Champions League titles in his first season.
When asked about Lucio's move to Juve earlier this week, Inter Milan president Massimo Moratti told 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."