Its Leeds office will build the 420-place schools in Shirecliffe and Fir Vale for Sheffield City Council.
BAM is now working on designs to meet the requirements of the council ahead of a start on site in September for completion in August 2014.
Construction director Kelvin Pollard said: “It is a great sign that BAM continues to be selected as a company trusted to deliver quality buildings at affordable prices through regional frameworks such as YORbuild.’
BAM has built a series of major education and health projects in Sheffield in the past ten years such as the Arts Tower and culminating in the laboratory rationalisation project for Sheffield Teaching Hospitals.