The 95,000 sq ft store will be built at Caldewgate in red standstone to blend in with the nearby castle and work is expected to start within two months.
Plans also include building a restaurant on a mezzanine floor above the supermarket and a petrol station and parking for 430 cars in front of the store.
The council has also granted granted separate planning permission for an 80,000 sq ft supermarket to be built off Wigton Road a mile or so away from the Sainsbury’s site.
That 12-acre plot is now set for sale on the open market with Tesco the favourite to buy the site.