Striker Ellison and defender King have been training with the club's academy in recent weeks and impressed enough during a trial spell at Turf Moor to earn themselves short-term deals.
The pair have signed contracts until the end of the season with a view to extending them if the period proves successful.
The pair signed contracts last night at The Brewery Field at a small celebration event along with their parents and representatives from both Burnley and Spennymoor.
Striker Ellison was understandably excited at the prospect of the next six months. He said: "I'm over the moon. It's a big step and a much higher standard than I've been playing. I've wanted to be a footballer since I was eight years old.
"Despite knowing a few clubs were interested, I knew Burnley was the right club for me after I went on trial there and got on well with the players and coaches.
"I have to say I’ve loved every minute of my time at Spennymoor. I will miss the lads and would like to say thank you to Gary Farley and Liam Clough for their coaching that has helped me improve as a player."
Centre-back King was also in high spirits after joining the Premier League club. He said: "After we enjoyed a successful run in the FA Youth Cup, myself and Craig went on trial with Burnley. It's every kid’s dream to play at a high level and make a living from playing football.
"Spennymoor has helped me develop as a player and a person, and I would like to say a big thank you to the coaches and management team who have pushed me every week."
The Moors` under-18 side enjoyed a run in the FA Youth Cup, which saw them read the Third Qualifying Round before narrowly losing to Football League Tranmere Rovers.
Under-18 manager Gary Farley has overseen Ellison and King's development. He said: "We are delighted for the boys as they have been a credit to themselves and the club and it's also a great coup for the academy”.