The store will become the centre point for the new £70m town centre, which will feature 24 new shops and restaurants.
A planning application for the new building, which will also boast 475 car parking spaces, was submitted in February.
Subject to permission being granted, construction work will start this summer with the store expected to open to the public by Easter 2013.
Mike Murray, senior development surveyor for St. Modwen, added: “The plans for Longbridge town centre have always envisaged a major foodstore, and to have agreed a deal with Sainsbury’s to fulfil this key requirement at such an early stage in the project is a massive accomplishment.”
The town centre plans also include an hotel and 40 apartments, together with the newly-created two acre Austin Park which, if approved, will lead to the opening up of the river Rea for the first time in 100 years.
Once complete, the town centre will establish a new heart for the community and a focal point for the overall £1bn regeneration of the former MG Rover works.
Over the next 15 years, the scheme is expected to create up to 10,000 new jobs and 2,000 new homes. To date, 5m sq ft of redundant buildings have been cleared across the Longbridge industrial site.