Manchester United were the first to make their way into the semi-finals on Saturday evening, though Ole Gunnar Solskjaer's side laboured to a 2-1 win over a 10 man Norwich after extra time, captain Harry Maguire netting a 118th-minute victor for the Red Devils.
Both games will be held at Wembley over the weekend of July 18-19.More news: Pakistans tour of England to go ahead despite positive coronavirus cases
Spanish midfielder Dani Ceballos netted an injury-time victor in a 2-1 win at Sheffield United, which had two goals ruled offside by video replay.
Elsewhere, Daniel Ceballos fired Arsenal semi-finals with a stoppage-time goal that sealed a 2-1 win over Sheffield United at Bramall Lane on Sunday. Ceballos pounced with a low shot, just four minutes after David McGoldrick had equalised from close range.
Arsenal, who have won the Cup three times in the last seven years, had taken the lead midway through the first half through Nicolas Pepe's penalty after Chris Basham's foul on Alexandre Lacazette. United defender John Egan's header early in the second half was also chalked off.More news: Xbox Series S could debut in August to put PS5 on notice
What time is the kickoff scheduled for the FA Cup 2019-20 Newcastle United vs Manchester City?
BBC pundit Alan Shearer conducted the draw during half-time in the last-eight clash between Newcastle and City at St James' Park.
The win means Arsenal have now qualified for the FA Cup semi-final for the 30th time, equaling the feat first achieved by Manchester United when they beat Norwich City 2-1 on Saturday.More news: UK could lockdown city of Leicester over virus fears
Southampton moved up one place to 13th and is a comfortable 13 points clear of the relegation zone.