BAM Construction North will refurbish 16,000 square metres of the eight-storey facility as well as providing new facades and mechanical and engineering services.
The library will be kept operational throughout the project.
Enabling works start this month, with the main scheme getting underway in November and completing by Easter 2014.
According to the project promoters, the scheme will result in ‘a modern, flexible, technology-enabled learning environment that reflects the changing role of libraries in the 21st century’.
BAM will hold suppliers days to attract local labour and draw apprentices from the area.
The contractor, which has offices in Leeds, has a rich history in Hull. It built St Stephen’s shopping centre in the city and is currently on site with Humberside Police headquarters.
University of Hull Librarian, Dr Richard Heseltine, said: “We are delighted to announce BAM as our main contractor on this exciting and transformational project. We have been impressed with the company’s track record on other projects, particularly on projects which involve the maintenance of public services during construction and look forward to working in partnership with BAM.”