Juve said in a statement they would pay an initial two million euros for the 31-year-old, who scored the winning penalty in the final shootout against France when Italy won the 2006 World Cup.
The fee, which the clubs had struggled to agree on for days, could rise to three million depending on appearances.
"The purchase of Fabio Grosso adds further quality to an already very competitive squad," Juve chief executive Jean-Claude Blanc said in the statement.
Grosso, who came to prominence at Palermo before enduring a difficult 2006/07 season at Inter Milan, returns to his homeland after two seasons with the seven-times French champions.
Juve coach Ciro Ferrara had highlighted the left back area as a position he needed to strengthen with Paolo De Ceglie better going forward than in defence and Cristian Molinaro the complete opposite.
Juve have been busy in the transfer window, snapping up Brazilian playmaker Diego from Werder Bremen, Felipe Melo from Fiorentina, Fabio Cannavaro from Real Madrid and taking Uruguay defender Martin Caceres on loan from Barcelona.
Second in Serie A last season behind Inter Milan, the Turin club are again likely to be the champions' main rivals this season and demonstrated their form with a 3-1 win at AS Roma on Sunday where Diego scored two fine goals.
