Construction of the teaching block will begin next month and the first classrooms will open in the third term next year.
The school board already has other property work planned, including new administration facilities and netball courts.
Northcote Primary has a roll of around 450, which can increase by 50 after the building programme.
The Ministry of Education has to find space for 107,000 more school children in Auckland alone by 2040 and planned housing intensification means pressure will be felt within existing city limits.
Last month Kaye announced a redevelopment of Newmarket School, a project that will include the country's first four-storey school block.
Population growth areas in Auckland include Warkworth, Wainui, Silverdale, Albany, Long Bay, Kumeu, Whenuapai, Scott Point, Massey, Flatbush, Takanini, Clevedon, Drury, Pukekohe and Pokeno.
And in Auckland's inner-city, apartment-dwellers are predicted to increase to 78,000 by 2040.