The contractor will construct two new buildings as well as refurbishing several others on the existing site at Middle Park Way in Havant for Hampshire County Council.
BAM was selected by the council last year for the full refurbishment of the neighbouring Havant Academy which is due to be completed by the end of this year.
The Park Community School project is the first awarded through the revamped Improvement and Efficiency South East framework.
BAM was one of eight contractors selected last summer for the framework which could be worth up to £4.5bn over four years.
Work is expected to start this summer and construction will take two years.
Construction director Bob Sanders said: “It is very pleasing to have secured work already through the hugely important IESE framework. This demonstrates that BAM is providing viable solutions to local authorities during the challenging economic climate.
“It is also great to be working on more projects on the South Coast, which is a very important area for BAM with our considerable staff base in the region and to work again with Hampshire County Council with whom we have developed a strong working partnership.”