It is a stellar draw, featuring the Cup’s three most successful sides, with Arsenal the record 13-time winners.
United, who beat Norwich to reach the last four, have won it 12 times, while Chelsea, who edged past Leicester in the quarter-finals, have eight wins.
Both ties will be played at Wembley on the weekend of 18 and 19 July.
The final is scheduled for Saturday, 1 August at the same venue.
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.
That game was taking place after Arsenal knocked out Sheffield United, with Dani Ceballos scoring the winner in the 91st minute.
The semi-final between United and Chelsea is a repeat of 2018 final, which was won by the Blues.