The four-storey building will form part of the wider Flemingate redevelopment project and will open to learners in September 2015.
Houlton have now begun work on site, with construction planned for completion in July 2015.
The contract was procured through the YORbuild framework, which provides public and third sector organisations with access to high quality construction firms.
“We now look forward to working with Houlton over the coming 15 months to deliver the state-of-the-art campus which will provide enormous benefits to Beverley and the wider region.”
Richard Houlton, chairman of Houlton, said:
“This award is great news for our company. To be part of a project that will shape the provision of learning opportunities for many years to come is a great privilege, and we look forward to a building ready for use for the 2015 student intake.”
The new campus will feature 30 teaching rooms with specialist IT facilities and a large Learning Resource Centre with access to a wide range of digital and printed reference materials.
It will also feature industry standard hairdressing and beauty therapy salons, a restaurant and a travel agency, which will provide realistic training facilities for students and be open to paying members of the public.
One key element will be the Energy Technology Centre, which will provide facilities for small to medium enterprises, corporate support services and links to training across a range of business, energy and environmental services.
The existing college campus in Gallows Lane will be developed by Peter Ward Homes, with 36 houses being built on the site, commencing in the autumn of 2015.