Grant, 23, has signed a six-year deal with the Premier League side, West Brom confirmed on Friday (AEDT).
The Englishman scored 19 Championship goals in 43 games for Huddersfield last season.
"We have followed Karlan's progression for a long time and has been a target of ours since well before the summer transfer window opened," West Brom technical and sporting director Luke Dowling said.
"We are confident we have signed a young player who has proved he is ready for the challenges of the Premier League. He has scored goals throughout his career including the few months he had with Huddersfield at this level two years ago.
"During this window we have largely focused on bringing in talented, young players, who have all committed to the club with lengthy contracts, and Karlan is one we are particularly delighted to have here for the foreseeable future."
Grant joined Huddersfield from Charlton Athletic in January 2019, netting four Premier League goals in 13 games as the Terriers were relegated from the top flight.
During that Premier League season, Grant scored once every 218.5 minutes, while converting two of his five big chances. He also created eight chances in his appearances.
Grant is West Brom's ninth signing of the transfer window as they bid for Premier League survival.
Slaven Bilic's men have one point from their opening four games to sit 17th in the table ahead of Monday's clash at home to struggling Burnley.