The semi-final clash between the rivals has been confirmed for a 6pm kick-off on Friday, May 14 at Villa Park and will be broadcast live on BT Sport.
The winners will host either Ipswich Town or Liverpool in the final, which is currently scheduled for Saturday, May 29.
Villa, who last lifted the trophy in 2002, are aiming to reach the final for the first time since 2010, when they were beaten by Chelsea over two legs.
Albion, meanwhile, have not reached the final since a team including Derek Statham beat Wolves 5-0 to win the competition in 1976.
Both clubs have made impressive progress through to this stage of the competition, which restarted in March after initially being halted at the start of the first lockdown in January.
Villa’s youngsters have scored 22 goals through four rounds so far, including 15 in the last two after following up a 9-0 win over Burton with a 6-1 thrashing of Newcastle in last month’s quarter-finals.
Albion began their campaign with a comfortable win over non-league Basford before going on to beat Cardiff and Tottenham, the latter an emphatic 5-0 victory.
They then came from behind to defeat Everton 2-1 and set up a last four showdown with Villa.
Meanwhile, the Express & Star understands that 6,000 Albion fans will be able to attend The Hawthorns for the club’s final home game of the season against West Ham in two weeks.
The contest, which takes place on Wednesday, May 19, will welcome 6,000 home fans if government restrictions on the roadmap out of lockdown are relaxed, with a decision expected on Monday.
The tickets will be made available via a ballot.