Sayes Court will double in size and provide an additional 210 places by September 2015.
Surrey County Council said it needs to "bridge a Â£215m funding gap" for 13,000 places, blaming an "unprecedented demand" on its services.
It said nearby Esher School is also being completely rebuilt to boost capacity by 210 places.
An artist's impression of how an expanded primary school in Addlestone will look has been unveiled.