The firm has beaten off stiff competition for the prized job from a line up of rival bidders, including Sir Robert McAlpine, Vinci and Miller Group.
The scheme being led by Spenhill Developments, the commercial property arm of Tesco, includes plans for new town square surrounded by 45 shops, offices, a 950-room student village and underground parking, as well as a Tesco store.
The Gastshead site was formerly home to an iconic multi-story car park, featured in the film Get Carter that was demolished by contractor Thompson earlier this year.
In recent years B&K has carried out several projects for Tesco, this is the biggest to date.