The Grade-II listed Fry Building, located just off the Triangle on the corner of University Road and Woodland Road, will undergo a major renovation and remodelling project.
The development is a key feature of the University's £525m 10-year capital investment programme.
While the intrinsic character of the historical building will be preserved, new additions will include an atrium to link a new 140-seat lecture theatre with a roof garden above it.
Further lecture theatres as well as offices and tutorial rooms will be created, as well as a wide variety of new spaces for interaction.
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The project is being managed by Capita Project Management, with architectural advice from the scheme's original designers Wilkinson Eyre.
Previously, the building was home to the School of Biological Sciences, which has relocated to a new £56.5m Life Sciences building.
Patrick Finch, Bursar and Director of Estates, said: "After an extended period of enabling works, dealing with a range of activities from demolition and site clearance within the heritage building, we are very pleased to have reached the point where contracts for the main construction works have been agreed.
"Balfour Beatty has been selected for its specialist knowledge and for the strength of the team put forward to manage the project for the University. We very much look forward to working with them in what we hope will be a productive partnership."
Professor Noah Linden, Head of the School of Mathematics, added: "The Fry Building will provide an outstanding home for mathematics in the heart of the University's precinct, and we are very excited about moving into it.
"We will have facilities for research and teaching befitting a world-leading mathematics department, in a unique Grade II listed building, remodelled and refurbished to retain its historic character."
The transformed Fry Building is due to open in October 2017.
(LM)
