The Belgian attacker has cut ties from Juve, as he has moved to Werder for a fee rising to €12m.
Mbangula said, "The discussions with the management and the coach have convinced me about Werder Bremen and the project they are implementing here.
"I can't wait to meet my teammates during the training camp and hope to be able to put my skills to good use right away."
Werder sporting director Peter Niemeyer said: "We are delighted to have been able to sign Samuel and that he has decided to stay with Werder Bremen long-term. We see great potential in him. He received an excellent education in Belgium and especially at Juventus, where he demonstrated his qualities at the highest level last season."
Niemeyer continued: "This is a transfer we have pursued with full conviction. We have always said we are willing to invest if we are convinced of a player and his potential. This is absolutely the case with Samuel. We are convinced that his qualities will benefit us directly."
Werder coach Horst Steffen also welcomed the Belgian: "Samuel brings good speed. He's very well-prepared both footballingly and tactically, can play various attacking roles, and thus makes our game more flexible . Now we need to integrate him into the team as quickly as possible. That's why it's a great decision that he's come directly to Zillertal."