The contractor was awarded the contract for Netley Street School by the local education partnership for Camden, as part of the borough's Community Investment Programme.
BAM will create a new school building on the existing site along with a playground and landscaping.
BAM will remodel an existing Victorian school building and install a lift to improve accessibility.
Other buildings have been demolished and the pupils and staff will be housed in temporary accommodation on the site for the period of the works.
Three floors of residential units will be built above the new school buildings, with a separate eight-storey block of flats taking the total number of private apartments to 70.
Sustainability measures including a combined heat and power plant, photovoltaic cells and natural ventilation will help the scheme achieve a BREEAM Excellent rating.
BAM construction director Mike Donegan said: “We are delighted to continue our long tradition of building in this area of London with this important facility for the local community.
“This project will create modern education facilities for pupils in Camden as well as much needed housing.”
Work is scheduled to be completed in December 2014.
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