The contract is for a fixed price build of £445M plus a allowance of £12 million should treatment works to mine workings along the corridor be required.
The project will now complete the road from Fullarton Road Junction, near Carmyle, to the M8 motorway west of the Kingston Bridge.
Transport Minister Stewart Stevenson said: "Following an internal review of the procurement processes the Government is confident the procedures are robust and we are happy for Glasgow City Council to award the contract to InterLink M74."
Consortium members are Morgan Est, Balfour Beatty, Morrison Construction and Sir Robert McAlpine.
Glasgow City Council Leader Steven Purcell said: "The bid achieves clear value for money against the independent cost comparator produced by consultants EC Harris on Transport Scotland’s behalf against current construction market cost."
Transport Scotland will manage the project which is likely to begin in May 2008. Completion is due at the end of 2011.