Demolition is expected to start within the new few months, with construction taking place over two years.
It is believed that BAM Construction is in talks to carry out the job.
By repurposing the Bordesley Street landmark, Stoford is aiming to deliver one of Birmingham’s first net zero carbon in construction office buildings.
The building will utilise the majority of its existing facades, structure and substructure, avoiding substantial carbon emissions.
The BBC is hoping to move from its current home at The Mailbox to the new 84,000 sq ft custom-built centre in 2026.
Typhoo Wharf will house several BBC editorial teams, including The Archers, BBC Asian Network, BBC Newsbeat, BBC Radio WM and Midlands Today.
Over the next decade, Stoford plans to deliver up to 800,000 sq ft of new residential, office and hospitality accommodation around the new BBC.
The wider scheme will see more than 10 acres of underutilised land around Typhoo Wharf and the adjoining canal basin transformed into a new mixed-use neighbourhood characterised by attractive public spaces and open thoroughfares.
A new public square will be delivered in time for the arrival of the first BBC staff.
Grant Associates is designing the new landscape and urban realm, which will create a new canalside quarter centred on the canal which used to bring tea in and out of the original Typhoo building.