Manchester United will take on Chelsea as Arsenal face Newcastle United or holders Manchester City in the FA Cup semi-finals.
With five Premier League teams remaining in the hat, the draw took place at half-time during City's clash with Newcastle at St James' Park – Pep Guardiola's side having taken a 1-0 lead into the interval thanks to Kevin De Bruyne's penalty.
United - who needed extra-time to see off Norwich City on Saturday, with Harry Maguire scoring late in a 2-1 win - were drawn first and will go up against Frank Lampard's side, who defeated Leicester City 1-0 on Sunday.
It is a repeat of the 2017-18 FA Cup final, which Chelsea won 1-0 under Antonio Conte.
Arsenal required a stoppage-time effort from Dani Ceballos to book their place in the last four, with the Gunners' winner against Sheffield United coming just four minutes after David McGoldrick had struck a late equaliser.
The semi-final ties will be played behind closed doors at Wembley Stadium on July 18 and 19, with the final scheduled for August 1.