The firm beat rivals Balfour Beatty, BAM, Miller, Morgan Sindall and Willmott Dixon, which were also swatting up for the student study centre.
Work on the four-storey building is set to begin this month, and the university hopes its Portland Stone finish will complement the iconic Parkinson Building.
The library will boast 1,000 study spaces, most with power points to support laptop use. The plans also include around 5km of shelving to accommodate core textbooks, two training rooms, an attractive café, and over 170 fixed PCs.
Contractor GB Building Solutions is also due to begin this month on the £8.5m refurbishment of the Social Sciences Building and will continue until autumn 2014.