Former Chelsea winger Boga will be on loan at Atalanta for the remainder at the season, though the move will be made permanent in the close season.
The Cote d'Ivoire international scored 18 goals and supplied seven assists in 98 Serie A games after joining Sassuolo from Chelsea in 2018.
Boga has attempted (152) and completed (80) more dribbles than any other player in Serie A since the start of 2021.
His 90 carries with a take on in the same timeframe is also the most of any player in the Italian top-flight, with only Adama Traore (145), Allan Saint-Maximin (122), Kylian Mbappe (113), Vinicius Junior (104), Neymar (102) and Yannick Carrasco (94) boasting more across Europe's top five leagues.
"I'm really happy right now and so is my family as we've wanted to come here for a long time. Now we're happy that the deal is done," Boga said.
"I think Atalanta are a great team, they are very strong and have proved to be an important team in Serie A over the past five or six years.
"I think it perfectly matches my style of play. I believe it's the right team for me to take another step and try to win something important.
"I know everybody expects something more from me and, at the same time, I expect myself to do better. I'm happy to be here.
"I know it's a solid team where everyone runs for the other, where each player works, and I think it's perfect, as you can see it's a real team."