The new school, to replace the existing St Flannan’s and St Agatha’s Primaries, will be built on the St Flannan’s site on Newdyke Road.
It is the third school to be built through the council’s controversial Primary School Improvement Programme (PSIP) and is scheduled to open in Spring 2017.
The application was lodged by the Council through architects Archial Norr and outlines in detail the layout of the building, its playground, Multi Use Games Area (MUGA), car parking and landscaping.
There were a number of objections from residents and parents to the plans.
Councillor Billy Hendry, Chair of the Planning Board, said: “The decision of the Planning Board enables the council’s Primary School Improvement Programme to take another important step forward.
“This is good news for the pupils of these two schools who will benefit from a school that is designed for the 21st century.”