The site, on Oxford Road, has been empty since 2012 when the BBC moved to Salford.
The project is being funded by a £36m special purpose vehicle from the Greater Manchester Housing Fund, taking the total invested in development projects across the region by the fund to £305m.
The fund will also invest £43m to Urban & Civic for 351 apartments at the junction of Princess Street and Whitworth Street in central Manchester, £22.5m to FICM for 380 apartments at the corner of Blackfriars Road and Trinity Road in Salford and £3.9m to Hillcrest Homes for 24 houses on the site of the Brethrens Hall in Heaton Mersey, Stockport.
Cllr Richard Farnell, Greater Manchester Combined Authority lead member for Planning and Housing, said: “Reaching over £300m of housing investment represents a major milestone for Greater Manchester. The Greater Manchester Housing Fund is a key part of our historic devolution deal and we are proud of the success we’ve had in supporting the creation of thousands of new homes across the city-region since 2014.
“The Housing Fund has allowed local leaders to kick-start construction and support developers in the creation of new, quality housing that our residents want and economy needs.”