The builder beat Balfour Beatty to the £16m job, which will involve demolishing 45-year-old buildings that house the Kind Edmund School.
Subject to full planning approval, work is planned to start on site next year, with the opening scheduled for September 2012.
Roger Gilbert, principal, Yate International Academy, said: “The staff, parents, students and governors of the Yate International Academy, will collaborate closely with the Willmott Dixon team over the next few months, to achieve the final design before the actual construction period.
“I would also like to thank our technical advisers, MACE and their team, for the quality of advice and support given to us so far, and we look forward to their continued involvement on the project.
The project was one of the academies to get approval from education secretary Michael Gove after months of uncertainty for the last two bidders.
In the region, the Government has also said it will invest in new buildings for the proposed Hans Price Academy in Weston-super-Mare and for Winterbourne International Academy.