BAM fought-off competition from rivals including Kier to bag the job at the Duke of York’s Royal Military School in Dover.
Work will involve refurbishing Grade II listed buildings and construction of several new structures.
The school became an “Academy with Military Traditions” in September 2010, and is now open to the children of both serving and non-serving parents.
BAM will demolish several non-listed blocks and build a sports hall, two two-storey teaching blocks and four two-storey junior boarding houses.
The contractor will also erect a two-wing, two-storey extension to Centenary House for senior boarders.
Further remodelling and repair work will take place across the estate including hard and soft landscaping and the provision of car park spaces.
Project director Rod Stiles said: “This scheme will provide cutting edge teaching, living and sporting facilities for students while remaining loyal to its historic roots.
“Most of the suppliers and construction workforce will be from Kent and our training programmes will continue to develop new local construction apprentices.”