The former Manchester United goalkeeper has signed a three-year contract with the Baggies.
The 29-year-old spent last season on loan with the Baggies.
Foster wrote on Twitter: “Really happy to have just signed for West Bromwich Albion, thanks to the fans for making me feel so welcome last year, can’t wait to get started.
“Want to say a huge thank-you to all at BCFC and the fans, will always look back at my time with you with fondness.
“I’ll never forget what you have done for me and will always remember the Carling Cup final as that meant so much to me, and you. My best wishes for the future.”
West Brom boss Steve Clarke told the club’s official website: “Ben’s been a priority signing all summer. His performances last season were exceptional and it was important for the club to strike a permanent deal for him.
“It’s a great signing for me and an even better one for the club. I think the supporters will be delighted we’ve been able to keep him on board – and make him our player.
“In any league in the world you want a goalkeeper that is going to make match-winning saves, turn draws into wins and defeats into draws.
“A quality goalkeeper is worth 10 or 12 points a season to you – and that’s certainly what we think we’ve got in Ben Foster.”
