The Galliford Try subsidiary will be working for hub South East Scotland Ltd a public/private development company on behalf of the City of Edinburgh Council.
The project involves the demolition of the existing school buildings and the construction of a new teaching block as well as new sports and theatre buildings on the campus over two phases. In addition, the Grade A-listed Bruntsfield House at the centre of the campus will be refurbished.
Completion is scheduled for summer 2016.
In addition to the construction contract, Galliford Try's facilities management business will provide hard facilities maintenance and lifecycle management services to the City of Edinburgh Council for the new school in a contract worth a further £10m over the 25-year concession period.
Galliford Try chief executive Greg Fitzgerald said: "Our relationship with hub South East Scotland Ltd is an important element of our Morrison business in Scotland and we are pleased to be selected for this significant education project for Edinburgh. We will continue to work with our public and private sector colleagues in Scotland to find innovative ways of delivering these projects that are so beneficial for local communities."