And two of the Magpies' young goalkeepers were also recognised in the seasonal shortlists, with Jake Turner nominated for the Under-23 Save of the Season and Oliver Marshall nominated for the Under-18 Save of the Season.
The shortlists were decided by the Premier League Football Development panel after club coaches nominated the best goals and saves by their players throughout the campaign, with all of the goals and saves available to watch on the Premier League website. Academy staff voted on the winners.
Anderson, 17, was named on the four-man shortlist for the Under-18 Goal of the Season prize for a great strike against Derby County, where he received the ball in his own half before driving forward, playing a one-two and brilliantly rounding the goalkeeper, but was edged out by Watford's Ryan Maclean.
And he was nominated for the Under-23 Goal of the Season for a fine solo goal against Scunthorpe United in a Premier League Cup clash - again, he was in his own half when he picked up the ball before a strong run ended with a delightful finish - but Manchester United's James Garner won the prize.
Anderson's grandfather, Geoff Allen, played as a winger for Newcastle United during the 1960s and was part of the squad which won the Inter-Cities Fairs Cup in 1969.
Teenage shot-stopper Marshall was nominated for the Under-18 Save of the Season for a block from point-blank range against Chelsea, but Aston Villa's Akos Onodi took the award.
And Turner was shortlisted for the Under-23 Save of the Season for a fingertip push onto the crossbar in a Premier League International Cup tie against Benfica. Henrich Ravas of Derby County won the prize.
Three Newcastle United Academy products - Matty Longstaff, Tom Allan and Kell Watts - made their debuts for the Magpies' first team in the 2019/20 campaign and Anderson, Turner and Marshall will hope to follow in their footsteps in the future.