Huddersfield have only won twice in their last 11 Premier League fixtures, but still sit 11th in the table.
The Terriers have agreed personal terms with Pritchard after an improved undisclosed bid for the 24-year-old had been accepted earlier in the week.
Pritchard has signed a three-and-a-half-year deal, which Huddersfield have the option of extending by a further 12 months.
"I'm very happy to be able to welcome Alex to Huddersfield Town", he told the Terriers' site.
After weeks of speculation, and having to increase their offer several times, the Terriers have secured their latest signing, and this time they've signed an English player from an English club.
'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'.
Pritchard progressed through West Ham's academy before switching to Tottenham aged 16 in 2009 and, after loan spells at Peterborough and Swindon, made his Premier League debut as a substitute in the final game of the 2013-14 season.
Wagner is hopeful of completing a £12million move for Pritchard ahead of the weekend.
Pritchard moved to Carrow Road from Tottenham for £8m in August 2016 and scored eight goals in 43 games, but saw his start to this season blighted by injury.