The matches will take place at Wembley over the July 18-19 weekend.
But City have been rampant against Arsenal in recent years, and beat Mikel Arteta's side 3-0 when they faced each other 10 days ago in the first game back from the coronavirus hiatus.
It took the Blues just a solitary goal just after the hour mark to book a semifinal spot, as Ross Barkley struck to drown Leicester City and set his side up for a clash against the league's' big guns.
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.
Substitutes made the difference as Chelsea and Arsenal both won away from home to reach the FA Cup semifinals.
The FA Cup semi-final line-up has now been completed after Manchester City defeated Newcastle United, and the Citizens' opponents have already been confirmed.
However, there was time for the Gunners to get the winning goal as Dani Ceballos surged into the box and sent a composed finish past Dean Henderson in the first minute of time added on to send his side to the last four. Ceballos pounced with a low shot, just four minutes after David McGoldrick had equalised from close range.
Forward Nicolas Pepe's penalty put Arsenal ahead midway through the first half, after United midfielder John Lundstram had an early header ruled out for offside. But 16th-place Watford remains one point above the drop zone with six games left.