The school is the third phase of the £41m Marlborough Hill Campus redevelopment where Bouygues is building the £11m George Eliot Primary School and Alternative Provision Centre.
The Quintin Kynaston job is the tenth and final school in Westminster City Council’s Building Schools for the Future programme.
Bouygues will start on the Quintin Kynaston contract when the two other schools are finished in December 2012.
Bouygues UK’s Jonathon Clarke said: “Quintin Kynaston signifies the final phase of this complex campus project which has required innovative design solutions throughout every aspect of the programme.
“We are really proud to have worked on such a challenging educational project which will significantly enhance the learning experience for teachers and pupils alike.”
The construction phase for Quintin Kynaston will take 34 months in total including demolition and landscaping, with completion scheduled for October 2015.