They are among a total of 30 firms making the cut on a panel that will be used to deliver an estimated £500m-£1bn of work over four years.
The LGSS construction framework will be open to all local authorities and public body clients. It will be used for repairs and renovation, refurbishment, demolition, modular build, extensions and new build.
LGSS is the shared services venture set up in October 2010 by founding partners Cambridgeshire County Council and Northamptonshire County Council, and ranks as one of the largest ventures of its kind.
The next venture for LGSS will be a major design consultancy framework, which is due to be launched for tender in the next couple of months.