The award follows on from a three-year Early Contractor Involvement collaboration between Costain and the council, which saw the the project become the first highway scheme to pass successfully through the new National Infrastructure Planning process.
The project will involve a full reconfiguration of Junction 34 of the M6, 4.8km of dual carriageway, 4.5km of new slip-roads, and 12 major structures including a 200m-span crossing of the River Lune.
When complete, it will connect Heysham and the Morecambe peninsula directly to the M6.
Work will start in January and is expected to complete in 2017.
Andrew Wyllie, Chief Executive of Costain, said: “We have worked closely with the Council and all local community stakeholders through the design development and planning process, and we now look forward to continuing the partnership to deliver an excellent outcome for Lancashire.”