Foster, who spent last season on loan at the Hawthorns, has moved to Albion for an undisclosed fee.
"Really happy to have just signed for West Bromwich Albion, thx to the fans for making me feel so welcome last year, can't wait to get started," the former Manchester United trainee posted on his Twitter feed.
The former England international has put pen to paper on an initial three-year contract with a further two-year option in the club's favour.
"Ben's been a priority signing all summer," West Brom manager Steve Clarke told the club's official website.
"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 ten or 12 points a season to you - and that's certainly what we think we've got in Ben Foster."