The contractor, which has offices in Leeds, will build the schools in Shirecliffe and Fir Vale for Sheffield City Council.
The schools are being built to meet rising demand for primary school places in the city. BAM is working on designs for the schools and is expected to start work on site in September.
Completion is scheduled for August 2014, which means the schools will open at the start of the 2014/15 academic year.
BAM beat three rivals to secure the work, which was procured through the YORbuild frame-work.
Construction director Kelvin Pollard said: “We look forward to using our experience and skills to create two schools Sheffield can be proud of.
“These are important facilities for the city and we are delighted BAM has been chosen to deliver them.
“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.”
Coun Jackie Drayton, Sheffield City Council’s cabinet member for children, young people and families, said: “Giving children the best possible start in their education is essential in helping them to reach their full poten- tial.
“These new schools will provide desperately needed places and put well-designed facilities at the heart of the community. It’s great to hear that work will be starting soon.”
BAM has worked on a number of major education and health projects in Sheffield over the last decade, such as the Arts Tower and the laboratory rationalisation project for Sheffield Teaching Hospitals.
In Rotherham, BAM is delivering the new Advanced Blade Casting Facility for Rolls-Royce.
BAM has been involved in a number of high-profile projects in recent years, including the new pavilion at the Yorkshire Cricket Ground in Headingley, Leeds, as well as the Leeds Arena.