The 24-year-old former Coventry City keeper has convinced Baggies boss Bryan Robson of his fitness during a two-week trial at The Hawthorns.
"Chris is a very talented keeper but he's got stiff competition here," assistant boss Nigel Pearson told the club's official website.
"I'm delighted for him because he's had a tough time with injuries and I know what that can be like. He's desperate for a run of games but he'll have to fight hard to get them."