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.

Elizabeth Bowe, 50, was found badly injured in Bobby Jones Place in St Andrews at about 21:00 on Saturday 17 September.
She was taken to Ninewells Hospital in Dundee but she died three days later.
Her brother Charles Gordon, 51, appeared at Dundee Sheriff Court on Tuesday facing a single charge of murder.
He made no plea or declaration and was remanded in custody.
The police were called out to Ms Bowe's home before the incident.
The Police Investigations and Review Commissioner's (PIRC) investigation was ordered by the Crown Office and Procurator Fiscal Service (COPFS).
A spokesman for the PIRC said: "The investigation will focus on the initial police response leading up to the incident.
"A report on the Commissioner's findings will be submitted to the COPFS in due course."
An artist's impression of how an expanded primary school in Addlestone will look has been unveiled.
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The police watchdog has launched an investigation following the death of a 50-year-old woman.