The Circuit of Wales scheme is backed by the Heads of the Valleys Development Company.
Construction work is expected to be technically challenging with the circuit built on a mountain-top site covering 830 acres of land in Blaenau, Gwent.
The deal is another coup for FCC who have ambitious expansion plans in the UK.
Rafael Foulquie, UK Managing Director for FCC said: “This project signifies a remarkable milestone within the company’s international development, and reinforces our vision of the UK as our main target.
“It’s a great opportunity for FCC to get established in Wales, promote local employment and work closely with local communities.”
Alun Grifiths director Martyn Evans said: “As a local Welsh company, it is a huge honour for Griffiths to be involved in the delivery of the Circuit of Wales.
“This is the sort of project that will change lives in Blaenau Gwent, as well as people’s perception of the area. We’re thrilled to be a part of it.”
Heads of the Valleys Development Company chief executive Mr Carrick said: “The people of Wales, and Blaenau Gwent in particular, should be really excited about what will be built.
“Having seen the work that our construction partners have done in the past, I’ve no doubt that the Circuit of Wales will be a diamond in the British sporting landscape.
“We chose these companies because of their vast experience, global renown and because of the superb team they can put in place.
“They fully grasp the Circuit of Wales concept and how to deliver it and share our vision and passion for making it happen.”
The development will include a 3.5-mile long racetrack, an international kart track and motocross tracks, together with a technology park adjacent to the circuit.
An application for planning permission is expected to be submitted next month.