The young Magpies booked their spot in the final, which will be staged at St. James' Park, after defeating North Shields 4-2 on penalties in the semi-final following a 1-1 draw at the Daren Persson Stadium.
Their reward is a tie against the Spartans, who compete in the sixth tier of English football, after the Green Army beat Bedlington Terriers 1-0 in the last four.
The two sides last met each other during a pre-season friendly in August as Blyth claimed a 3-0 win at Croft Park in front of 1,148 spectators.
Newcastle have won the trophy a record 38 times, with their most recent cup triumph coming back in 2018 after United's youngsters claimed a 3-1 victory against Morpeth Town at St. James' Park.
A date and kick-off time for the cup final will be announced in due course.