The contractor will demolish the existing single-storey school buildings in Bridgwater and replace them with a two-storey 1,300m2 building.
BAM will also convert another building on the site into a nursery, which will be connected to the new school building.
Additionally, there will landscaping works to the sloping site, including the provision of a winding 70m-long pathway.
Work starts on site during half-term next week with completion in October 2014.
During the construction period, pupils will be decanted into accommodation at neighbouring school sites.
BAM Construction worked on both sites under the Bridgwater Schools scheme, where it now provides facilities management services, and sister company BAM FM is refurbishing a building at Chilton Trinity to accommodate Penrose pupils.