The first leg will be played at Goodison Park on Wednesday 6 January (8pm), while the second leg will take place at the Etihad on Wednesday 27 January (7:45pm).
City have come up against the Toffees twice in the League Cup, winning one and losing one.
The Blues beat Everton 2-1 on the way to winning the competition in January 1970 and the Merseysiders inflicted defeat on City at the quarter-final stages in 1988.
Everton have never won the competition but have finished as runners-up twice, 1976/77 and 1983/84, while City are looking to lift the trophy for a fourth time.
Manuel Pellegrini’s side booked their place in the last four of the competition thanks to a 4-1 win over Hull at the Etihad Stadium on Tuesday night.
Wilfried Bony opened the scoring and Kelechi Iheancho netted the second before Kevin De Bruyne bagged a brace to complete the scoring.
Liverpool will meet Stoke City in the other Capital One Cup semi-final.
Semi-final ticket details will follow in due course.
