Albion will be away to Tottenham Hotspur in the fourth round of the Emirates FA Cup.
The teams last met in the competition in 2005 when Spurs won 2-1 in a third round tie at White Hart Lane. Richard Carpenter equalised for Albion after Ledley King put Spurs in front, but Robbie Keane got a late winner for the home side.
The tie will take place on the weekend of 4-7 February. Further information will be announced in due course.