The 17-year-old centre half has linked up with the Toffees, committing his future to the Goodison Park outfit having spent his formative years on Tyneside.
Gibson, the younger brother of United Under-23s’ full back Liam, was part of the Magpies’ Under-18s side last season.
He was part of United’s FA Youth Cup run last season as Dave Watson’s youngsters made it to the last eight, and has also played for the club’s under-23 team and been capped by England at under-17 level during his time at St. James' Park.