The scheme will also see Tesco build a new library on the site of the former East Durham College, off Burnhope Way.
The proposed £12m store will follow the Tesco Environmental Store Format.
This means it has been designed to deliver more than 50% carbon savings, a third less energy consumption, will use low energy LED lighting and be built to a BREEAM Very Good standard.
The main structural frame will be made of glulam timber and it will be powered using gas combined heat and power plant.
The planning consent comes as new research shows that planning approvals for large retail development jumped by 36% in the last quarter of 2010, compared to the same period a year before.
The rise will bring a welcome surge in fresh orders for builders this year, according to Giles Ferin, head of planning at EMW, the commercial law firms that released the research.
The expansion is being largely driven by Tesco and Sainsbury’s, with Asda and Waitrose starting to ramp up their new store conversion and opening programmes.