Everton will face either Manchester United or West Ham in the FA Cup semi-finals, while Crystal Palace will take on Watford.
The ties will be played on the weekend of April 23-24 at Wembley.
Manchester United will travel to Upton Park for a quarter-final replay after the sides drew 1-1 at Old Trafford.
The date of that last-eight replay will be announced after the second leg of United’s Europa League last-16 tie against Liverpool on Thursday.
Everton beat Chelsea 2-0 on Saturday to reach the last four for the first time since 2012.
The other semi-final is a repeat of the 2013 Championship play-off final, which Palace won thanks to a Kevin Phillips penalty.