Aquilani is currently head coach of US Catanzaro, whom he guided to fifth place in Serie B last season — the best finish in the club's recent history.
His appointment at Sassuolo represents a step up in category, with the Emilian club having stabilised in Serie A after finishing eleventh this season.
The former Italy international midfielder brings a strong playing pedigree to the role. During his career he represented Roma, Juventus, AC Milan, Liverpool, Fiorentina, Pescara, Sporting Lisbon and Palermo, winning Serie A titles and the Coppa Italia before moving into coaching.
His work in the lower divisions of Italian football — including a two-year spell at Pistoiese before Catanzaro — has earned him a reputation as a technically demanding and tactically clear-headed coach.
Grosso's departure to Florence, where he signed a two-year deal with an option for a third, opens the managerial vacancy at a club that also faces the imminent sale of centre-back Tarik Muharemovic, heavily courted by Inter Milan and Como this summer.