The matches will take place at Wembley over the July 18-19 weekend.
Manchester United sealed their place in the last four on Saturday when they won 2-1 away at Norwich after extra time, as Harry Maguire struck with two minutes left to play against the hosts, who went down to 10 men late in the second half.
Sheffield United's Oliver McBurnie (R) reacts after a FA Cup sixth round loss to Arsenal.
The draw was made at half-time in the game between City and Newcastle, which Pep Guardiola's side won 2-0 thanks to a Kevin de Bruyne penalty and a classy Raheem Sterling finish.
Record-holding, 13-time winners, Arsenal also made it into the last four after Dani Ceballos netted a stoppage-time victor for Mikel Arteta's side after Sheffield United's David McGoldrick had equalised following Nicolas Pepe's first-half penalty.
The hosts' David McGoldrick netted on either side of goals from Nicholas Pepe and Dani Ceballos, with the latter scoring at stoppage time.
Arsenal responded with an injury-time victor through Dani Ceballos to seal their return to Wembley and move two wins closer to lifting a first trophy under Arteta, who was appointed Unai Emery's successor in November.
That victory was needed to give Arsenal some form of confidence having lost back-to-back games against Manchester City and lowly-rated Brighton.
Either Manchester City or Newcastle United will make up the final four.