The 32-year-old spent the latter part of last season with Burnley, helping the club to the Premier League, and becomes West Brom's third signing of the close-season.
Baird's deal includes a performance-related option for a further year and he follows Joleon Lescott and Craig Gardner to The Hawthorns.
A versatile defender who can play across the back four as well as in midfield, Baird has top-flight experience with Southampton and Fulham.
He will be tasked with helping West Brom, in their first season under new head coach Alan Irvine, improve on an underwhelming 17th-placed finish last time out.
"Chris is a player with vast Premier League and international experience who reads the game well and has good positional sense," Irvine told West Brom'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."
