The builder confirmed it has won the £40m Watling Academy through its LGSS framework agreement.
Graham will build a three-storey main building with an adjacent sports hall and sports pitches and playing fields.
It will use BIM to design and manage the 86-week construction programme of the 10.88-hectare site.
Staines civils contractor Euro-City Group is delivering the drainage and concrete package, with Rhyl-based building services specialist on the MEP package.
Rob Joyce, Graham’s London office director, said: “This new secondary school will be an important education centre for the Western Expansion Area of Milton Keynes, supporting its future development and attracting more families to the area.
We will use the knowledge and experience we’ve gained from our extensive education portfolio to deliver an outstanding new facility for the local community.”
The Denbigh Multi Academy Trust (MAT), which currently operates through Denbigh School, will operate Watling Academy to deliver the high-quality secondary education curriculum.