Di Francesco left the club on Tuesday and Sassulo, 18th in Serie A, have opted for Malesani, whose most recent coaching role came at Palermo, as his successor.
A statement on the club's website read: "Sassuolo Calcio announces that it has entrusted the task of coaching the first team to Mr. Alberto Malesani.
"Mister Malesani will direct the team's training this afternoon (Wednesday)."
Milan vice-president Adriano Galliani claimed on Tuesday that the club's youth-team coach Filippo Inzaghi had been a target for Sassuolo, but the strugglers have opted for 59-year-old Malesani.
He has spent almost all of his managerial career in Italy, venturing abroad for a spell with Panathanaikos in 2005, but lasted less than a month with Palermo before being sacked last February.
Sassulo have won just one of their last eight Serie A matches.
Malesani is due to take charge of his first match against Verona on Sunday.
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