Kent Count Council named Willmott Dixon as its preferred contractor back in November 2010. The contract was finally signed on 15 July.
Completion of the building, designed by architects Studio E, is scheduled for early 2013.
Willmott Dixon Construction managing director Mark Tant said: "Reaching financial close on the project is a major milestone and we are pleased that construction can now begin. It is an ambitious project and we are fully committed to ensuring that the new facilities will be a source of pride and an inspirational place for learning.”