The contract is part of a £300m revamp of the tube station and main construction work will get underway in 2011.
The job will take six years to complete and will link Bond Street with new Crossrail stations at Davies Street and Hanover Square which will be let under separate contracts.
Laing O’Rourke and Costain’s contract includes building a new entrance and ticket hall north of Oxford Street and installing new escalators.
The winners fought off competition from Balfour Beatty and a Taylor Woodrow / BAM Nuttall joint venture.
Kulveer Ranger, the Mayor of London’s transport advisor, said: “This station emphasises the need for progress to be maintained on both upgrading the Tube and building Crossrail.”
David Waboso, Capital Programmes Director for London Underground said: “By 2017, Bond Street station will be served by both London Underground and Crossrail and will be a key gateway to the West End.
“This redevelopment is essential to ensure the station can accommodate the large increase in passengers that will use the station.
“The £300m redevelopment of the Tube station, coupled with the new Crossrail station, will transform the Bond Street area and act as a catalyst for further investment securing the West End’s position as a premier shopping and entertainment destination and major employment centre.”
The Bond Street job is the latest in a series of major contracts let by TfL.
The £500m redevelopment of Tottenham Court Road Tube station went to Taylor Woodrow Construction and BAM Nuttall.
This was followed by a contract for the £700m redevelopment of Victoria station to Taylor Woodrow Construction and BAM Nuttall Limited Joint Venture in March.