The Non League side thrashed Wimbledon 3-1 away in a replay on Tuesday night., after the two sides had shared a goalless draw at the first attempt.
Sutton are the lowest ranked team left in the famous competition and lie 15th in the National League Premier.
The London club inserted an artificial 3G pitch at Gander Green Lane in the summer of 2015.
Leeds have met Sutton only once before when Allan Clarke's four goals saw the Whites run out 6-0 winners, also in the FA Cup fourth round.
United reached the fourth round with a 2-1 win over Cambridge United earlier this month.