Foster left Birmingham City last week.
The 29-year-old was voted the supporters' player of the year and players' player of the year in helping the Baggies finish 10th in the Barclays Premier League.
Foster said: "The fans accepted me so well and I always got such an amazing buzz off them last season.
"I've got a special connection with them and joining the club was a bit of a no-brainer because of that.
"I'm quite a positive person and give everything all of the time and I think the fans appreciate that.
"They were with us throughout, were our 12th man at times and sometimes you need that."