A problem with the building came to light during a routine inspection earlier this year, when it became apparent that stonework in the gable ends had shifted. Some stonework has already been removed and further stonework removal is scheduled for later this month.
Contractors will rebuild two granite gables and that work is due to begin on Monday [13 August] and be completed in early November.
The school will re-open as normal to staff on August 20 and to pupils on August 21.
Council leader and Enterprise, Planning and Infrastructure convener Barney Crockett said: "Our experience at Woodside School highlights the importance of carrying out building inspections. Safety is a priority for the council.
"I am pleased to see such good progress being made with the repair work and am sure that the pupils and school staff will enjoy watching the contractors at work and seeing the progress they make as the months go on."
Pupils will not be able to enter the works area.