Armstrong, 34, joined the club in the summer of 2016 after winning back-to-back promotions with Darlington FC, and has scored 15 goals in fifty-one appearances for Spennymoor.
He was part of the squad that won promotion to the National League North via the play-offs last season.
The vastly experienced target man started out with Scottish side Annan Athletic before joining Ebac Northern League side Dunston UTS.
He became their record goalscorer which led to a move to Gateshead for an undisclosed fee.
After helping the Tynesiders to promotion to the National League, he then joined Harrogate Town before spells with Blyth Spartans and Whitby Town where he scored over 30 goals in one season, winning the `golden boot` award.