Albion have been drawn away at AFC Bournemouth in the third round of the Emirates FA Cup.
The tie is set to take place at the Vitality Stadium across the weekend of 11/12 January 2025.
The Cherries, managed by Andoni Iraola, are currently 13th in the Premier League.
The two clubs have met twice before in the world's most famous cup competition, with each team claiming one victory.
They last met in the FA Cup in January 1999 when Bournemouth triumphed 1-0.
A date and kick-off time, as well as ticket details, will be confirmed at the earliest possible opportunity.