The Terriers agreed a compensation fee with United for the 21-year-old Northern Ireland international, who has signed a three-year contract at the Galpharm Stadium.
"I'm over the moon to have become a Huddersfield Town player," Norwood told the club's official website. "I met with the manager and after speaking to him and the chairman there was only ever one club I was going to join."
He added: "His ambition for the club matches where I want to take my career and I see this move as the best step for me. I had been at Manchester United from the age of seven and I love the club - it was always my dream to play for United - but there comes a time when you have to be realistic."
Norwood spent the second half of last season on loan at Coventry, who were keen to keep hold of him, but opted for Huddersfield ahead of the Sky Blues and Yorkshire rivals Barnsley, who had also agreed to meet United's compensation fee.
Norwood, who made 18 appearances for Coventry last season, is confident the Terriers can push for another promotion, saying: "I think we can have a real go at the Championship this season and, you never know, maybe follow in the footsteps of Norwich and Southampton.
"Looking at the squad and who the manager wants to recruit there's no reason why we can't be challenging for promotion."