Professor Thomas will take over from the incumbent, Steve Smith, vice-chancellor of the University of Exeter, on 1 August next year and will remain in post until 2013.
The former consultant gynaecologist, who is currently vice-president of UUK, said it would be a “great honour” to represent the umbrella group during a time of massive upheaval in the academy.
“The sector faces challenge and opportunity in equal measure and UUK will ensure that higher education’s voice is heard and its strategic value recognised,” he said.
Professor Thomas, who graduated in medicine from Newcastle University in 1976, has been vice-chancellor of Bristol since September 2001. Before that he was a dean at the University of Southampton.
He is also chair of the board of the Council for Advancement and Support of Education Europe and chaired a government task force that considered how to increase voluntary donations to universities, which reported in 2004. In 2009, Professor Thomas announced that he had donated £100,000 to Bristol in a bid to lead by example.
Nicola Dandridge, chief executive of UUK, said: “Eric will bring tremendous commitment, knowledge and experience to the role of president, and we are all looking forward to working with him in the future.”