Redundant warehouse buildings on the site in Falsgrave Road will be knocked down to provide space for the 20,000 sq ft extension.
The firm will also totally refurbish the existing store adding features such as new flooring and ceilings as well as improved staff facilities.
Outside, the car park and access roads will be resurfaced while the service road will be relocated to provide better access.
An eco-friendly rainwater harvesting system will be installed to recycle rainwater for use within the building.
The supermarket will continue to trade throughout the 34-week project where Barr plans to use as many local subcontractors as possible.
Paul Happell, project manager at Barr Construction, said: “The extension and refurbishment will provide local residents with an up-to-date store and brand new facilities.
“We have delivered many similar projects for Sainsbury’s across the UK and this experience will allow us to keep disruption to a minimum for staff, shoppers and the surrounding community.”
Barr recently completed an extension for Sainsbury’s Kingsgate store in East Kilbride and successfully delivered all work without having to close the store.
Scarborough residents can expect the Sainsbury’s store to be finished by the end of October this year.