The online betting company will sponsor the Club's shirts for Monday's home match with QPR (ko 7.45pm), which is live on Sky.
This is the first time a company has commercially sponsored Albion's shirt for a selective game.
Blue Square contacted Albion after the Club announced two weeks ago it was ready to open talks about ground-breaking match-by-match shirt sponsorship deals.
For the second season running, the team have been playing in unsponsored shirts as the Club's search for a suitable, long-term, official sponsor continues.
However, after receiving clarification from the Football League, Albion can offer businesses and organisations the unique opportunity to sponsor their shirt for single or multiple games.