Blanc left his post "by mutual agreement" on Monday after a 4-1 home defeat against Paris Saint-Germain.
He took over in October 2022. Not counting interim coaches, Grosso is the fifth club manager since June 2019.
Lyon finished seventh last season to miss out on European competition for the second year running.
The team for Sunday's Ligue 1 match against Le Havre will be prepared by one of Blanc's assistants, Jean-Francois Vulliez.
Grosso was a key player in the Azzurri's World Cup triumph in Germany 17 years ago.
He netted the opening goal in Italy's semi-final win over the tournament hosts and then the winning penalty against France in the final.
Grosso also won Serie A titles with Inter Milan in 2007 and Juventus in 2012.
He started coaching with Juventus's youth system in 2014 before continuing his modest managerial career mostly in the Italian Serie B.
He joined Bari in 2017 staying one season during which he revealed a dead rooster was left outside his home as a threat by rival fans.
He also had brief spells at Hellas Verona, Brescia and Swiss club FC Sion, before joining Frosinone in 2021, guiding them to Serie A promotion last May.
With Lyon, he can ease in with a seemingly favourable schedule with matches against Reims, Brest, Clermont and Lorient between now and the next international break.
