The clubs boast 32 FA Cup wins between them, with Arsenal leading the way with 12.
Chelsea secured their place in the last four when they knocked out holders Manchester United 1-0 at Stamford Bridge on Monday night.
Arsene Wenger’s side Defeated non-league Lincoln 5-0 at the Emirates on Saturday, while Manchester City ran out 2-0 winners over Middlesbrough at the Riverside to secure their place at Wembley.
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Tottenham breezed into the semi-finals with a 6-0 win over Millwall at White Hart Lane on Sunday.
Arsenal and City have met just twice before at any stage in the competition, with their most recent meeting coming in a 2-1 fifth-round win for the Gunners in 1971.
City have not lifted the trophy since 2011, while Arsenal enjoyed back-to-back wins in 2014 and 2015.
The Blues and Tottenham met at the semi-final stage in 2012 when goals from Didier Drogba, Juan Mata, Ramires, Frank Lampard and Florent Malouda secured a 5-1 win for the Stamford Bridge side.
Arsene Wenger will be looking for silverware to help ease some of the pressure on his shoulders, while Antonio Conte will be determined to end his debut campaign at Stamford Bridge with a domestic league and cup double. Spurs have not won the FA Cup in 26-years.
The ties will be played at Wembley Stadium on Saturday, April 22 and Sunday, April 23.