Under the £18.5m contract it will also refurbish the adjoining Queensferry Primary School.
Building work will start in July 2015 with the new schools scheduled to open in January 2017.
The contract has been let under the new North Wales Schools and Public Buildings Contractor Framework procurement process.
Cllr Chris Bithell, Flintshire County Council’s cabinet member for education, said: “I am delighted that our latest new 21st century learning campus is progressing and that work is due to start on site within the next 12 months.
Together with the new Holywell Campus and the Sixth Form hub at Connah’s Quay we are developing first-class educational facilities for the children and young people of Flintshire.”
Gary Wintersgill, managing director of Kier Construction’s northern operations, said the firm would be engaging with the local supply chain and offering local training and apprenticeship to provide a lasting legacy for the local area.