Midas Construction has been appointed to carry out the first phase renovation project, which involves an extensive overhaul and internal refurbishment to create a new University reception and student study centre.
The flagship facility, which spans five storeys and 2,643 square metres, will accommodate up to 350 seats for student group and individual study.
A large bright reception and café space will be open to the public, providing a focal point for all visitors to the University, including prospective students and parents.
Beacon House will become a key part of the University's campus thanks to its location between the Students' Union on Queen's Road and various teaching and research activities around Tyndall Avenue and Woodland Road.
Professor Guy Orpen, Deputy Vice-Chancellor at the University of Bristol, said: "This is a really exciting project for the University as the building is in such a prime position, allowing us to not only provide vital study space but also to welcome in the public and showcase some of our success stories."
The project is the latest in a series of investments by the University in teaching and research facilities, totalling in excess of £200 million in the last two years.
Patrick Finch, Bursar and Director of Estates at the University, added: "We are delighted to be working with Midas on this high profile project. Beacon House is currently a very tired building but it will be transformed over the next nine months into a fantastic space for students, staff, visitors and the public."
Derek Quinn, the Executive Director of Midas Construction, said: "The project has many challenges and through close collaboration with the University stakeholders, we have developed a solution to meet the expenditure and time constraints. We now look forward to delivering an industry leading performance throughout the delivery stage."
Beacon House, next to the Royal West of England Academy, was constructed in the 1850s and was formerly the Queen's Hotel before being used for retail purposes – Gardiners in the 1930s, Debenhams after the war and more recently Habitat, which closed in 2011.