The 25-year-old Dutchman, who also had offers from the Premier League, has struggled to make an impact in Antonio Conte's first team since moving to Turin from Hamburg last summer, and had long been linked with a return to the Bundesliga.
"I actually had several offers from England and from the Bundesliga," Elia told Bremen's official website. "However, I settled on Werder because I have very good feelings here.
"Werder are an offensive team and that will suit me. The Bundesliga is one of the strongest leagues and I'm looking forward to the season.
"The teams are more attacking here and my strengths will be better suited. It was difficult in Italy, where the teams are very concerned about a stable defence."
However, the Bianconeri and the player have now come to an agreement, and Elia has moved to the Weserstadion in a deal that will be paid over a two-year period.
ADO Den Haag, Elia's first club, will receive around €300,000 (£238,000) for their part in nurturing the Netherlands international's talent. He also represented Twente in his homeland.
Werder Bremen have also brought in Theodor Gebre Selassie and Nils Petersen this summer.