The development is being constructed by Blackfriars Group, which secured planning permission and also owns the site.
Sainsbury's will be taking on a lease over the building and car park once the shell construction work is completed.
The company said work remains on track for the store to be handed over in the Autumn to enable it to be fitted out before officially opening in time for Christmas.
The 18,000 square foot store, at the junction of the A49 and Rocks Green, will also include an Argos store.
Once complete, the store will provide 160 car parking spaces and is expected to create about 150 jobs across a range of roles and levels.
The supermarket said it will also play an active role in the local community and will be supporting Sainsbury’s nationwide community programmes.
In January the supermarket chain announced an additional £1 million community fund for stores to donate to charities and other good causes in their local areas.
It follows the Help Brighten a Million Christmases campaign that raised £6 million in December for more than 800 local charity partners, Comic Relief and FareShare.
Patrick Dunne, Sainsbury's property director, said: "I know the community will really enjoy seeing their new store come to life over the summer months.
"This will be a fantastic state-of-the-art store and gives the local community more convenience and greater access to our high quality, great value products.
"We are proud of this major investment into the local are and will continue to keep everyone updated on this exciting new store, including how to join the local colleague team."