The project will see Willmott Dixon extend both ends of the existing academy building to create a new sixth form facility and additional dining facilities.
The extension is due to open in September 2009.
The job, part of the national academies framework, will be carried out by a Willmott Dixon team from its Dartford office.
The company was appointed under the BSF Academies Framework after Mossbourne was given permission by the DfES to create a Sixth Form.
Mossbourne Community Academy was designed by the Richard Rogers Partnership and is the first academy in Hackney.
Willmott Dixon (Dartford) managing director Rob Lambe said: “The team are really looking forward to enhancing what is already an outstanding place to learn.
“Alongside Studio E, we have a team that is very experienced in creating excellent environments to learn and teach and look forward to adding to Mossbourne Community Academy already impressive facilities.”