He takes over as Chancellor of the global top 50 University from The Right Honourable the Baroness Hale of Richmond, who has held the role since 2004.
Sir Paul is a leading geneticist and cell biologist. His work on the control of cell division underpins current research into treatments for cancer and other serious diseases.
His contributions to science were recognised with a knighthood in 1999. In addition, Sir Paul's endeavours relating to the discovery of molecules that regulate the cell cycle saw him jointly awarded the Nobel Prize for Physiology or Medicine in 2001.
Sir Paul said: "I felt very honoured to be asked to Chancellor of the University of Bristol. It is one of the UK's great universities, both in terms of its world-leading research and also its teaching. With the recent announcements about its new campus and ambitious plans outlined in its new strategy, it’s an exciting time to be involved."
Over the last 30 years, Paul has held many senior research leadership roles. He was Director General of the Imperial Cancer Research Fund and then CEO of Cancer Research UK.
He was appointed President of Rockefeller University in New York in 2003 and was elected as President of the Royal Society in 2010 for a five-year term.
Since 2011, Sir Paul has been the Director and Chief Executive of the Francis Crick Institute, based in London and one of the largest biomedical research institutes in the world, which opened in 2016.
As Chancellor of the University of Bristol, Sir Paul will be the ceremonial head of the institution and play an important ambassadorial role, nationally and internationally.
Professor Hugh Brady, Vice-Chancellor and President of the University of Bristol, said: "To have Sir Paul as our next Chancellor is a huge honour. He has an unrivalled standing in the scientific community, in this country and across the world. He will be a great inspiration for our staff and students.
"His appointment could not have come at a more opportune time, as we look forward to the next step in our University’s development. I very much look forward to working with him over the coming years."
Sir Paul will be installed as Chancellor on 22 March 2017, during a special ceremony in the Wills Memorial Building.
Previous Chancellors include Viscount Haldane, originator of the Haldane Principle, former Prime Minister Sir Winston Churchill, Sir Jeremy Morse, who provided the inspiration for Inspector Morse, and Nobel Prize-winning scientist Professor Dorothy Hodgkin.