The Baggies confirmed last week that the 33-year-old defender would not be offered a new contract at The Hawthorns this summer.
Reid arrived at West Brom from Blackburn Rovers in 2010 and went on to score four goals in 87 appearances for the team.
"It's been an honour and a privilege to play for those supporters and my teammates as well," he told the club's official website.
"I've been lucky enough to be in a dressing room that's been full of great lads who have wanted to work hard, improve themselves, improve the club and make sure we've had success in every season."
Burnley and Queens Park Rangers are among a number of clubs who are thought to be keen on signing Reid for next season.