Blues booked their place in the last four with a 2-1 home win in their quarter final tie against Aston Villa on Wednesday night whilst the Hammers overcame Manchester United 4-0 at Upton Park on Tuesday evening.
The first leg of the two-legged semi final will be played at Upton Park week commencing 10th January 2011 with the second leg at St Andrews taking place a fortnight later.
In the other semi-final Arsenal will play Ipswich Town.