Boateng only turned 31 in March but the Ghana international has spent his career at nine different clubs, which now becomes 10 with the switch to Sassuolo.
The former AC Milan player has a partner who is from Italy, and the ex-Tottenham Hotspur and Portsmouth man is keen to settle in the country after linking up with the Serie A outfit.
Frankfurt sporting director Fredi Bobic told the Bundesliga's official website: "I agreed with Prince when we signed him that we would never stand in his way if he wanted to leave. He expressed that wish now because he would like to be playing where he sees himself settling to live, which is why I have obviously kept my word.
"We have a lot to thank Prince for. He was an outstanding leader, both in human terms and sportingly, and we wish him and his family all the best for the future. Kevin-Prince Boateng leaves Eintracht and the Bundesliga as a winner."
Boateng scored six goals in 31 top-flight appearances last season.