Anderson, who lives in Whitley Bay, joined United's youth system at under-nine level after starting out with Wallsend Boys Club.
The attacking midfielder, who turned 17 this week, has agreed terms on his first professional deal. His grandfather, Geoff Allen, played as a winger for Newcastle United during the 1960s and was part of the famous squad which won the Inter-Cities Fairs Cup in 1969.
Anderson, who has three international caps under his belt with Scotland under-18s, has already played for United's under-23 squad this term and made his debut in the Leasing.com Trophy against Macclesfield Town as well as starring in United's under-18 side that reached the Super Cup final in Northern Ireland last summer.
Academy Manager Joe Joyce said: "Elliot deserves this. He has pushed on this season in the under-18s, and has started to score goals on a more regular basis.
"His performances have caught the eye of the Scottish FA, and he's had international call ups for their under-18s. As a result of his good work, he's also had opportunities with the under-23s this season, and he's certainly not looked out of place.
"He's a real determined individual and he knows that there's still a lot of hard work to be done, but he thoroughly deserves his first professional contract."