The plans break new ground as the first free school and sixth form college run by a university.
The university is building its own secondary school to help city children from all backgrounds into top institutions.
Willmott Dixon is understood to have beaten Galliford Try, which was also chasing the two-year building job, due to start in a few months.
Its purpose-built 1,150-pupil school will be located at the University’s Selly Oak site, close to the main Edgbaston campus and a wide range of University facilities.
It will also be one of the first university training schools, boasting better teacher student ratios from embedded trainee teachers from the university.