Albion will face Brentford in the third round of the Carabao Cup on Tuesday, September 22.
The tie will kick-off at 7pm at The Hawthorns.
The Baggies reached round three with a comfortable 3-0 victory at home to Harrogate.
The Bees needed penalties to squeeze past Wycombe in the first round before securing an impressive 2-0 win away at Southampton in round two.
The winners of the third-round tie will be at home to either Fulham or Sheffield Wednesday in round four.