The deal is the first for a University Technical College (UTC) in the South West.
The academy will specialise in Engineering and Environmental Technology and provide facilities for 440 students from Bristol, Bath, South Gloucestershire and North East Somerset.
Willmott Dixon will demolish the old Filton High School in Stoke Gifford, Bristol before starting on the new build.
The building will house large workshop areas needed for increased levels of vocational project work as well as smaller classrooms, laboratory areas and indoor sports facilities.
Externally, there will be a multi-use sports area and parkland where ecological studies can be undertaken.
John Boughton, operations director of Willmott Dixon in the South West, said: “We are very excited to be involved in the establishment of the South West’s first university technical college, which will prove a significant boost to the already fantastic educational provision in Bristol.
“This will also help develop the city’s existing reputation in advanced engineering and sustainable technologies, while boosting employment opportunities in these burgeoning vocational sectors.
“In addition, the development itself will open up local job opportunities and provide a boost to the local economy through our use of locally sourced materials and local subcontractors.”
Willmott Dixon secured the contract through the Scape framework.
The academy is due to open on 2 September 2013, with work finishing for the start of the 2013 term.