The 23-year-old has penned a three-year deal and becomes the Canaries' sixth addition of the summer.
Husband, who began his career at Doncaster, has played 62 times at Championship level but made just one Premier League appearance for Boro last season. He has previously had loan spells at Fulham and Huddersfield.
Husband told Norwich City TV: "I'm delighted to join such a big football club. First and foremost I've come here to play football and to enjoy my time as much as possible. The main thing is to try and get Norwich up the league as far as we can go."
Husband's arrival follows the signings of Marley Watkins, Mario Vrancic, Christoph Zimmermann, Harrison Reed and Angus Gunn at Carrow Road this summer.