The 32-year-old spent the latter part of last season at Burnley - helping the club to the Premier League - and becomes West Brom's third signing of the close-season after Joleon Lescott and Craig Gardner.
A versatile defender who can play across the back four as well as in midfield, Baird has top-flight experience with Southampton and Fulham and new manager Alan Irvine is confident he will improve his squad.
"Chris is a player with vast Premier League and international experience who reads the game well and has good positional sense," 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.
"We have done our homework on him. I have spoken to a lot of different people who have either managed or played with Chris and everyone spoke very, very highly of him both as a player and a person."