The 28-year-old will replace Scott Carson, moved to Turkish side Bursaspor earlier this summer.
"We are very, very happy that the deal to bring Ben from Birmingham has gone through," West Brom boss Roy Hodgson said.
The former Manchester United keeper was relegated from the Premier League with Birmingham last season, although he was named as the official man of the match in their Carling Cup final win over Arsenal.
Hodgson added: "We are confident Ben is the goalkeeper we need to help us enjoy a successful season in the Premier League."
Foster has made five appearances for England but is currently taking a break from international football to concentrate on his club career.
The Baggies' new number one may make an appearance in today's friendly with Bristol City at the Ashton Gate Stadium.