Balfour Beatty said its joint venture with construction company VINCI has won two contracts worth a combined GBP2.50 billion, under which it will deliver Lot N1 and Lot N2.
The seven companies to win contracts also included Emirates and Olympic stadium builder Sir Robert McAlpine, Balfour Beatty and France's Vinci. Grayling said in his statement that the civil works are expected to support 16,000 jobs and generate 7,000 contract opportunities, of which around 60% were expected to go to SMEs.
The overall budget was revised up to £55.7bn, but estimates drawn up earlier this year on behalf of Lord Berkeley, chairman of the Rail Freight Group, who had argued at select committees for alternative routes for HS2 out of London, suggested it could be as high as £111bn.
Phase one will consist of two stages, the first of which involves design and construction preparation, and is already underway.
But Transport Secretary Chris Grayling said the higher figure is "just nonsense".
Mr Cochrane confirmed in a separate announcement that professional services EY was being brought in to "bring an external perspective to our cost reduction and cash collection challenge".
The work includes the North Portal Chiltern Tunnels to Brackley, worth £724m, and the Brackley to Long Itchington Wood Green Tunnel South Portal, worth £616m.
He said his priorities were to "reduce the group's net debt and create a balance sheet that will support Carillion going forward".
A bill will be published shortly covering phase 2a - from the West Midlands to Crewe and which is expected to open the following year - while phase 2b from Crewe on to Manchester begins in 2033.
Ministers suggested in November previous year that the line should serve the existing Sheffield city centre station, after proposals to run trains to the Meadowhall shopping centre were shelved.
The route of the Manchester and Leeds section of HS2 will also be announced later. Joe Rukin of Stop HS2 referred to the project once again as a "white elephant", saying "The case for HS2 has been invented by the very cheerleaders who intend to rake in billions of taxpayers' money which is desperately needed elsewhere".
But critics have warned this will mean homes on the new Shimmer housing estate in nearby Mexborough being bulldozed.
This will see 11 new high-speed platforms created as well as the redevelopment of 13 existing Network Rail stations. In a media interview Monday, Grayling rejected a weekend report by a quantity surveyor who claimed HS2 will cost nearly double the current estimate, taking the final bill to over 130 billion US dollars.