The 18-year-old put pen to paper on a three-year contract at the Weserstadion on Wednesday, having previously been with the German champions and Augsburg before that.
Husic made appearances for a host of Bayen's youth teams but failed to break into the first team at the Allianz Arena.
And he has expressed his excitement at signing for Bremen, who finished 12th in the Bundesliga last term.
"It's a really, really great feeling to be here and to have signed my first professional contract," he told the club's official website.
"I am very much looking forward to the task with Werder Bremen."
Husic has also played regularly for Germany's Under-17 team during his time at Bayern, with Bremen's director of football and scouting Frank Baumann keen to point out the need for the goalkeeper to develop further.
"Raif is a very talented goalkeeper and he will have the chance to develop further still with us," he added.
"Although he is still eligible to play for the Under-19 team, we intend to use him in the Under-23 side and give him the opportunity to train regularly with the first team."
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