The controversial scheme to build the 120,000 sq ft store at St James Industrial Estate will also include a petrol filling station, car wash and more than 700 parking spaces.
The Enquirer understands the Scottish contractor beat Vinci and ISG which were also bidding for the project.
Greatline, the developers behind the project, has pledged to spend £1m upgrading transport and pedestrian links with the town centre.
The new store, which is to be built about 1km from the town centre on the site of former steelworks slag heaps, won planning last February despite being opposed by many local businesses claiming it would have a negative impact on trade.
This included objections to the development by town centre landlord Land Securities, which is backing a bid for a Sainsbury’s supermarket in Corby.