The blaze broke out on Friday evening, and firefighters worked through the night to contain it.
A 14-year-old boy has been arrested on suspicion of arson, and police are searching for another two teenagers in connection with the incident.
Thousands of Eastfield residents and their families attended the school over the years.
The school moved to a new site in July 2021. Since then the building has been empty, but there were hopes it could be turned into a community venue.
Borough councillor Tony Randerson said: “I’m absolutely devastated about it. This is an area that is targeted for community use in the future, rather than even more homes built on there and more houses.
“The day it happened, on Friday, I was talking to North Yorkshire County Council estates regarding the concerns about it being broken into, vandalism, etc and reiterating that I expected that planned site to be designated for community use rather than houses, and the same evening the massive fire took place and it really shocked me. It’s something that you don’t expect.
“When I saw the video clips, I went first thing on Saturday morning to talk to residents on Hawthorn Walk. If the wind had been the same ferocity as had been the week before, then the houses on Hawthorn Walk could well have been affected. I’m devastated.
“The vast majority of Eastfield residents who were brought up in Eastfield have been here 60 years, and more, and they all went to that school so they’re very upset about it. They’ve got lots and lots of memories of happy days at that school which have been taken away from them.
“They’re well aware the school had shut, but they were hopeful that it could be turned into something beneficial for the community and now that’s been taken away from them.”
The fire has upset the local community, with many people having fond memories of the school, as a pupil themselves or as a parent.
Local resident Samantha Wilshire said: “I walked past the school yesterday and it is heartbreaking to see. The school is in the middle of the community, not just in the position but in the centre of many families for generations. Many social media posts show that the school may have been taken but their memories will be there forever, which can be seen by all the photos and words of the community.”
“It's horrible, my boys don't understand why some people would do this. They said it's lucky no-one was there, that it is very dangerous.”
On our Facebook page, former pupil Joanne Smith commented: “I went there from 1967-1973 when Mr Bedford was headmaster then he left and in came Mr Rayner. It was a lovely school back then.”
Another former pupil, Tina Marie, shared a memory of the school on Facebook, saying: “I think our headmaster was called Mr Raynor. At our assemblies he would shout, "Tempus fugit" and we would shout, "Time flies". Also our school trip to Belgium, good times! “