The young Magpies booked their place in the final after beating Northern League Division One outfit North Shields in the semi-final stages via 4-2 on penalties following a 1-1 draw at the Daren Persson Stadium.
United's second-string, who also beat Newcastle Benfield and Ashington en route to the final, will face Terry Mitchell's Spartans, who claimed a 1-0 win over Bedlington Terriers in the last-four stage at Croft Park.
The two sides met in the competition back in February 2019, with Newcastle recording an emphatic 7-2 win over the Green Army at Whitley Park in the quarter-finals.
Newcastle's youngsters last lifted the trophy in 2018 after defeating Morpeth Town 3-1 at St. James' Park.