Telford & Wrekin's planning committee has approved plans which will see the land turned into 123 houses.
Councillors were disappointed that the plans provided no affordable housing, but were told the community benefit in the proposal will be that funds raised from the plans will go to paying for the new replacement school.
Residents living near to the former school site in Trench were concerned about the proposed entrance to the site, close to Trench Tots nursery and about the design of housing being built, hoping to see bungalows, in keeping with the current housing developments.
But plans approved at the meeting held on Wednesday at the Whitehouse Hotel, were only outline, which means details like the entrance and the houses will be decided at a later date.
Councillor Nigel Dugmore said: "I would suggest that this is a very good development of a brownfield site. But it is very irritating, as it is with any development, that there is no affordable housing provision. That said, it would be crazy not to develop the site.
"When detailed plans do come forward, I hope they take notice of concerns regarding the access, the size, scale and mix of dwellings."
The loss of the school means the end of a local link with the successful conquest of Everest, the world's highest mountain.
Sutherland Co-operative Academy, as it was known in its final guise, closed on July 3 last year.
It has been amalgamated with Wrockwardine Wood Arts Academy and opened for the autumn term as a combined new school in new buildings in Oakengates, known as Telford Priory School.
The Sutherland had opened as Trench Boys' Secondary Modern School on January 24, 1955. Sir John Hunt, who led the expedition which conquered Everest in 1953, agreed to be the new school's "godfather" and as its patron made a number of visits in which he spoke to children and on one visit joined them for tea and biscuits.
It was renamed the John Hunt School in July 1973. Then in October 1994 the Sutherland School was created by the merger of the John Hunt School and The Manor School, Hadley, on the John Hunt site.
Meanwhile work to demolish Wrockwardine Wood school is nearing completion. Again, the site is earmarked for housing.