Bovis beat off a bid from Schal to win the prestige contract, due to be completed in 2008. Building tipped Bovis to get the job in October.
A BBC confirmed the appointment, but denied reports that the scheme would be funded directly by the corporation through TV licence income. It said: "We are negotiating the procurement route, but to say it is funded by the licence payer is not the case."
The BBC is in talks over Broadcasting House with developer Land Securities Trillium, which is already undertaking the £300m redevelopment of the BBC's White City studios in a PFI-style deal.
The MacCormac Jamieson Prichard-designed project at Broadcasting House was originally expected to follow a conventional construction management route but a new deal is now expected to be struck in March.
To say the development is funded by the tax payer is not the case
Subject to that deal, the contract is likely to change from construction management to guaranteed maximum price. One source said: "Construction management is just a temporary arrangement."
Project sources said that the delay in the Broadcasting House decision, initially expected in July, had not held back the redevelopment. Bovis is understood to have built up its team before the official announcement.
The contractor last week issued tenders for trade packages such as electrical and building maintenance services. Demolition is expected to start next month.