Foster enjoyed a successful season on loan at Albion before moving for an undisclosed fee on an initial three-year contract which also includes a further two years in the club's favour.
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."
Foster was linked strongly with a move to Queens Park Rangers before it snapped up
But he insisted: "There were never any worries that I'd be going anywhere else. Everyone knows how happy I was here last season.
"There were rumours circulating about other clubs but it was nothing I never took seriously because my family were settled in the area."
English Premier League
Departing Everton defender