The seven times winners will face the London club, with manager Carlo Ancelotti making his first visit to the national stadium.
The other semi-final, also to be played at Wembley, saw the winners of Fulham and Tottenham Hotspur meet the 2008 FA Cup winners Portsmouth.
The favourites Chelsea beat Stoke City at Stamford Bridge 2-0 courtesy of goals from Frank Lampard and John Terry.
Aston Villa, who visited Wembley last month for the Carling Cup final, came from 2-0 down at half-time to book themselves another date in the captial by beating Reading 4-2.
Shane Long struck twice for the struggling Championship side, before Ashley Young replied for Villa just 70-seconds after the re-start and towering striker John Carew scored a hat-trick.
On Saturday, Fulham held Tottenham Hotspur to a goalless draw at Craven Cottage to force a replay, while the Premier League's bottom club Portsmouth lifted their spiritis by beating Birmingham City 2-0 at Fratton Park thanks to a brace from Frederic Piquionne.
FA Cup semi-final draw (in full):
Aston Villa v Chelsea
Tottenham Hotspur / Fulham v Portsmouth