The committee approved the application on Monday 6 October for the new £21.8m facility at Nethershot on Angraflat Road.
Work on the new school, which will include new grass and synthetic sports pitches and community facilities, is now expected to begin in early 2015.
Councillor Sandy Aitchison, SBC's Executive Member for Education, said: "I am delighted the planning application has been approved for Kelso High School.
"I am sure the people of Kelso will be looking forward to a modern facility being built which will benefit generations of schoolchildren and the local community."
Paul McGirk, Chief Executive of the Council's development partner, Hub South East Scotland Ltd, added: "It's exciting to reach this major milestone in the development. The new Kelso High School will allow pupils and staff to enjoy modern, fit-for-purpose facilities and the community will benefit from investment in the local area.
"We look forward to continuing our successful partnership with Scottish Borders Council to make these plans a reality."
A land purchase agreement between the Council and land owners Lothian Estates for the ground at Nethershot on Angraflat Road was concluded in March.
Hub South East Scotland appointed Morrison Construction as its preferred contractor last year to construct the school and both held a Meet the Buyer event in July for local businesses to find out how they can get involved in the project.