New Bracken House will provide 270,000 sq ft of Grade-A office accommodation.
No official value has been put on the contract but rival firms approached by the Enquirer suggested it would be worth around £100m.
Work will involve the complete strip out of the building with some portions of the floors on the wings removed to create open courtyards.
The external listed wings will be cleaned and refurbished and the existing roof configured with a 150 metre running track for employees, encasing a glass skylight.
The fit-out comprises full catering facilities and over 1500 desks in open plan offices as well as audio and video studio suite and live broadcasting capability, including a news room.
Domonic Egan, Operations Director, McLaren Construction London said: “The New Bracken House Project is a challenging and exciting addition to our current workload in London and further strengthens McLarens credentials as a leading contractor for commercial office buildings including CAT B fit out.
New Bracken House is owned by the Obayashi Corporation and is situated at 1 Friday Street in the City of London, next to St Paul’s Cathedral.
Bracken House was occupied by the Financial Times newspaper until the 1980s when the company moved to Southwark.
The building was partly demolished in 1989 to incorporate the Michael Hopkins glass and steel façade that is evident today.