"Born in Berlin on 6 March 1987, Kevin-Prince Boateng is a player who will surely adapt quickly to the team", said Barcelona on their official website.
The 23-year-old midfielder has a contract until 2020 and has also been linked with AC Milan.
Barcelona will be Boateng's fourth club in the past three seasons, though the former Ghana worldwide has fared well at each of his stops.
Speaking to Sky Sport Italia, Boateng said: "It's a bit of a sad day, because I leave a fantastic group and a club like Sassuolo that gave me so much". The France forward's injury further reduces Valverde's attacking options going into the two-legged Copa del Rey quarterfinal against Sevilla and league games against Girona and Valencia.
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Powell's time at United was plagued by injuries but he did score on his debut at Old Trafford against Wigan in September 2012. As well as the new signings, Celtic are going to be without three big players for them.
He's also played for Eintracht Frankfurt and Las Palmas in the last few years, but there were no signs of a potntial move to a giant European club. Denis Suarez, despite Valverde's reluctance to let him go, is still keen on a move to Arsenal, while the club are open to offers for Brazil forward Malcom.
Previously he played for Las Palmas in the 2016-17 campaign but left for family reasons.
Boateng - formerly of Tottenham Hotspur and Portsmouth - has contributed four goals and one assist in 13 Serie A outings this season.