Graham Potter will take his squad to Kenilworth Road on Saturday, July 31, kick off 3pm.
The Hatters finished 12th last season in their second campaign back in the Championship.
They are managed by former Albion player and coach Nathan Jones, who had a brief spell as the club's caretaker boss in 2014.
Ticket details for the fixture will be announced shortly, but Luton hope to be able to offer tickets for visiting fans.
Albion face Scottish champions Glasgow Rangers in their opening pre-season game next Saturday (5.30pm).
They also face La Liga club Getafe at the Amex on Saturday, August 7, kick off 7pm.