Their third-round tie at Manchester United will take place on Sunday, January 11 with a 4.30pm start.
It will be shown live on TNT Sports and Discovery Plus.
Travelling fans have also been given ticket details.
Adults will pay £55 (or £44 for season ticket holders).
Those aged 66 or older or 18-20 pay £41.25 (£33 for season ticket holders).
Ages 16-17 pay £27.50 (£22 for season ticket holders) and it is the same for under-16s other than season ticket holders get a further £2 reduction.
The selling process gets under way on Monday and full details can be found on the club website.
The cup tie comes four days after Albion have visited Manchester City in the Premier League.
Manchester United are at Burnley on the same evening.
Albion have at least avoided the Friday night slot, which goes to Wrexham v Nottingham Forest (7.30pm, TNT).
They are also spared the Monday night berth, which has been handed to Liverpool v Barnsley (7.45pm, TNT).
Saturday’s schedule starts with Macclesfield v Crystal Palace (12.15pm, BBC1 and TNT), followed by Spurs v Aston Villa (5.45pm, BBC1 and TNT) and Charlton v Chelsea (8pm, TNT).
On Sunday, armchair fans can enjoy Derby v Leeds (12pm, TNT) and Portsmouth v Arsenal (2pm, TNT) ahead of the prime-time action from Old Trafford.
Extra-time is played in the third round if ties are level after 90 minutes and there is a penalty shoot-out if needed.