Dave Watson's youngsters progressed thanks to a 4-1 win at Portsmouth in the third round earlier this month, as goals from Owen Gallacher, Lewis McNall, a Theo Widdrington own goal and Callum Smith gave United the victory at Fratton Park.
And their reward is a home tie against the Swans, which has now been set for Monday, 9th January and will be played under the lights at St. James' Park.
It will be the first time Watson's side have played at the stadium this season, and admission will be free for all supporters.