The decision means that construction work can now commence on the project from early next year.
The replacement building will be located at a new site in Cowan Park, which is next to the current school.
Alongside the new school, the council has said that the Johnny Kelly Pavilion, which is located at the old building, will be replaced on a new site in Cowan Park. The skate park will also be moved.
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When completed, they will be part of a sports campus that will also include a new running track, pitches, a 3G pitch and a cricket wicket.
Initial plans for the development will be submitted this week it is understood, with work scheduled to commence in July 2015. It is anticipated that the project will be delivered in December 2016.
Councillor Elaine Green, Convener for Education and Equalities, said: "This is wonderful news for the young people, staff and parents of Barrhead High.
"There will be absolutely no compromise on the quality of provision – the existing design for the building can be used with just a few tweaks so it will be the superb school we have always promised.
"Barrhead High pupils will get the school that was always intended for them – and that they deserve."
(JP/IT)
