The 40 Under 40 starlets have come up with a scheme which will sit on a backland plot in among the existing college buildings.
The development will feature rainwater harvesting, solar collectors and a solid-timber superstructure.
Practice partner Oliver Smith said: 'The project is a dense piece of urban infill that we believe will transform a fragmented site in the middle of Cambridge.
'We are delighted that the project has been given the seal of approval by the local authority.'
The Cambridge-based practice worked with structural engineers Michael Hadi Associates and environmental engineer Max Fordham on the development.