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.
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.
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