Albion have made Cardiff City's Kenneth Zohore their first permanent summer signing.
The 25-year-old former Danish U21 international has signed a four-year contract at the Baggies and will wear the No.9 shirt.
He becomes Albion's second addition of the summer after Croatian Filip Krovinović joined from Benfica on loan earlier this month.
"He is a player who has got more than a bit of everything, he's strong, he has pace, he has good skill," Slaven Bilic told the club's official website.
"He knows the league, he knows the country, he's already got good experience but he's still got room to improve. He's not the finished article.
"I hope he's going to be a very good player for us."