The 21-year-old moves to Serie A after winning two FA Youth Cups as well as UEFA Youth League and Under-21 Premier League titles while at Stamford Bridge, making just one senior appearance for the Blues since joining the academy from Marseille in 2009.
The midfielder impressed during loan spells with Rennes and Granada but his only outing for his parent club came in the shock 3-2 defeat to Burnley on the opening day of the Premier League last season.
Sassuolo, who finished 11th in Serie A in 2017-18, will reportedly pay a fee in the region of £3.5 million for the Ivory Coast international.
Goal revealed this week that a deal had been agreed between the two sides that includes a buy-back option for the Blues.
The winger had already attracted interest from Lille, Celta Vigo and Real Betis. Boga hoped to remain in London if he had a chance of regular first-team football, but he opted to leave on a permanent basis instead of being sent on a fourth straight loan spell.