The 32-year-old joins the Baggies on a free transfer after being released by Burnley at the end of last season.
Baird spent the final two months of the 2013-14 campaign at Turf Moor following spells with Fulham and Reading.
"Chris is a player with vast Premier League and international experience who reads the game well and has good positional sense," West Brom boss Alan Irvine told the club's official website.
"He can play in several positions and his versatility effectively makes your squad bigger. It's important we have the right characters in the dressing room and Chris is certainly that."
Baird has won 65 caps for Northern Ireland since he made his international debut back in 2003.