It is GB’s second award procured through the YORbuild framework, the construction framework for Yorkshire and Humberside.
The works will transform the existing 19th century industrial buildings of the Print Works in central Leeds into phase one of a new city-centre campus for the college.
Work starts on site this month with a construction programme of 43 weeks.
The scheme will provide a range of building types and spaces designed for the catering & hospitality and hair & beauty departments.
GB Group chairman and chief executive Martin Smout said: “Working together with Leeds City College, we are able to preserve part of Leeds’ industrial heritage and at the same time use modern building techniques to benefit the city for years to come.
“We are also able to offer valuable employment and skills opportunities to students across a range of departments and in this way we can have a positive impact both on the local community and the lives and career prospects of a number of young people."