Blanc was sacked last Monday after a poor start to the season that left the club bottom of the Ligue 1 standings. Former Italian international Grosso, who played for Lyon between 2007 and 2009, will take charge next Monday.
"The former Italian international defender, World Cup champion in 2006, has committed to the club until June 30, 2024, with the option to extend his contract for an additional season," the club said.
He led the club to the Italian Serie B title last season, gaining promotion to Serie A, but Grosso chose not to renew his contract there.
Lyon's next game is at home to Le Havre on Sunday.