Sheppard Robson will take over the second phase of the project - the new build - which will massively increase the floor space of the corporation's central London headquarters.
The practice can expect to face criticism for accepting the appointment, coming as it does just 12 days after MJP was dropped amid rumours that their design had been dumbed down.
It emerged last week that Bovis Lend Lease - the contractor to whom MJP was novated - and Land Securities, which was acting as a property partner to the BBC, had carried out a series of value-engineering exercises on the original competition-winning design.
Sheppard Robson's appointment will see the firm take over the new build proposed by MJP and a number of interior fit outs.
Bovis Lend Lease UK director Peter Jacobs attempted to put a positive spin on the new appointment. He said: 'The Broadcasting House scheme is designed to be an inspiring, flexible home for the BBC as it leads the way as a fast-evolving 21st century broadcasting service.
'We are pleased to welcome Sheppard Robson onto the team as we move into the next stage of this ground-breaking project.
'This will involve the incorporation of highly complex, detailed design features and the integration of cutting-edge technology and we look forward to working together with them and the BBC to complete the project,' Jacobs added.