The Terriers have agreed personal terms with Pritchard after an improved bid for the 24-year-old had been accepted earlier in the week.
“We’re delighted to announce that @pritch_93 joins £htafc from @NorwichCityFC for an undisclosed free, signing a three and a half year deal,” Huddersfield revealed on Twitter.
Pritchard could make his Terriers debut in Saturday’s home Premier League game against West Ham.
“Huddersfield Town has today completed the permanent transfer of Alex Pritchard from Sky Bet Championship side Norwich City,” read a club statement.
“The 24-year-old moves to Yorkshire for an undisclosed fee, putting pen to paper on a contract running until the summer of 2021, with a further year’s option in Town’s favour.”
The Terriers are reported to have paid between £10million and £14m.
Head coach 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 Sky Bet Championship and with a desire to prove himself in the Premier League.
“Now we will work hard with him to give him every possibility of being a success for us in the top division.
“I’d like to thank (chairman) Dean Hoyle and the board for being as supportive as ever in this transfer window and making this transfer possible.”