The fee has not been disclosed but it is understood to be in the region of £12million.
Pritchard has penned a three-and-a-half-year deal with the Terriers, with the club holding an option to extend it for a further year.
The 24-year-old scored eight goals in 43 games for Norwich after arriving from Tottenham in 2016.
Huddersfield Town boss David Wagner said: “I’m very happy to be able to welcome Alex to Huddersfield Town.
“He is exactly the type of player that we like to work with at this Club. Alex is a young, British player who arrives as one of the top performers in the Championship and with a desire to prove himself in the Premier League.