Roberto Martinez's men progressed to the last eight with a 2-0 win at Bournemouth on Saturday, while Chelsea cruised to a 5-1 victory against a young Manchester City side at Stamford Bridge on Sunday.
The last-eight clash is a repeat of the 2009 final in which Louis Saha opened the scoring for Everton after 25 seconds, only for goals from Frank Lampard and Didier Drogba to turn the match in Chelsea's favour.
Chelsea's current interim boss Guus Hiddink was also in charge for that match.
West Ham's reward for a 5-1 win at Blackburn is a trip to Shrewsbury or Manchester United, who go head to head in the fifth round on Monday night.
Arsenal will play Watford at the Emirates Stadium if the Gunners can get past Hull in a fifth-round replay at the KC Stadium
Reading will host Crystal Palace in the other last-eight clash, with matches to be played from March 11 to 14
Source : PA
Source: PA