Albion will play their Carabao Cup second-round tie against Derby County at Pride Park on Tuesday, August 23 (ko 7.45pm).
The Baggies progressed from the first round of the competition via a 1-0 win over Sheffield United at The Hawthorns on Thursday night.
Derby confirmed their place in the second round courtesy of a 2-1 win over Mansfield Town at Field Mill on Tuesday.
Albion last faced the Rams in the competition back in September 2000, with Derby earning victory over two legs, winning 5-4 on aggregate.
Ticket details for the trip to Pride Park will be announced on Monday morning.