The Netherlands international, 25, leaves the Italian champions after one unhappy season at the club.
Elia signed for Juventus from Hamburg last summer but made only one start in Serie A as he failed to make any sort of impression on coach Antonio Conte.
He underwent a medical with Bremen on Sunday and joined up with the club for a training camp in Norderney in the north of Germany on Monday.
Though formal confirmation of the transfer was initially delayed, Juventus announced on their official website on Tuesday morning that Elia had returned to the Bundesliga.
In two seasons with Hamburg the former FC Twente and ADO Den Haag midfielder scored seven goals and claimed 10 assists.