The game will be played on Monday 1 April at the Academy Stadium, with kick-off at 7pm.
City booked a place in the last four with a fine 4-1 win away at Bournemouth in the last round, while West Brom were involved in a seven-goal thriller, beating Everton 4-3.
The Baggies currently sit 10th in the U18 Premier League table.
The game is priced at £3 Adults, £1 Concessions and free to seasoncard holders.
The competition rules have changed this season and the Semi-Final will be one leg. The game will go to extra time and penalties if the game is tied at the end of 90 minutes.