Grant has signed a six-year deal with the Baggies, who described the 23-year-old as a 'long-term transfer target' on their website.
Technical and sporting director Luke Dowling said: “We have followed Karlan’s progression for a long time and he has been a target of ours since well before the summer transfer window opened.
“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 focussed 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 originally joined the Terriers in January 2019 and scored four Premier League goals in 13 appearances as his new side were relegated from the top flight.
An impressive season in the Championship followed, with the striker netting 19 goals in 43 league appearances.
Grant has previously played for England's Under-17, Under-18 and Under-19 sides and got his start at club level with Charlton, originally catching Huddersfield's eye with his performances in League One during the first half of the 2018/19 season.
Slaven Bilic's side had made a number of signings previously this summer. Among the permanent incomings were attacking midfielder Matheus Pereira, former West Ham prospect Grady Diangana, back-up goalkeeper David Button, forward Callum Robinson and ex-Chelsea star Branislav Ivanovic.
Conor Gallagher and Filip Krovinovic were also brought in on loan deals from Chelsea and Benfica respectively.