The national contractor, which has offices in the capital, will build new premises for Middle Row Primary in the Royal Borough of Kensington and Chelsea.
The building will hold up to 420 children aged four to 11, incorporating a speech and language centre. There will also be a nursery with a capacity for 30 younger children.
BAM will construct the facility in the grounds of the existing school.
Learning spaces will be more modern, comfortable and aesthetically pleasing as BAM brings the school into 21st Century facilities.
The scheme will include natural ventilation, solar panels, and a green roof.
BAM won the project through the Improvement and Efficiency South East framework.
Completion and operation of the school building is scheduled for spring 2014, followed by external landscaping completion in Autumn 2014.
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