The current vice-chancellor of the University of Leeds will take over from Malcolm Grant in September 2013, who retires having led UCL since 2003.
Professor Arthur, who was chairman of the Russell Group of research-intensive universities until August this year, is also a commissioner for the US-UK Fulbright Commission, a council member of the Medical Research Council, and deputy chair of the Worldwide Universities Network.
Chair of UCL Council, Sir Stephen Wall, said that the council chose Professor Arthur because they were impressed by his personal qualities, record of professional and academic attainment and by his leadership and achievements at Leeds.
"He has transformed Leeds University's research and teaching, established healthy finances, put Leeds on the map as a Russell Group institution and developed a strong sense of community and commitment among academic and non-academic staff," said Sir Stephen.
"He has a strong record of engagement with the local community. He has made Leeds a high performer in teaching, reflected in its ratings in the National Student Survey. He has not been afraid to take difficult decisions and to lead from the front but he also has a proven record of empowering others at all levels," he added.
Professor Arthur said it was a "very great honour" to be appointed.
"I admire the history and origins of UCL and the continued focus on its founding principles and values. Malcolm Grant will be a very hard act to follow, but I look forward to rising to that challenge in leading 'London's Global University'," he said.
Professor Arthur, whose research focuses on the liver, graduated in medicine from the University of Southampton in 1977, before becoming a research fellow and lecturer at the institution and eventually becoming dean of Southampton's Faculty of Medicine, Health and Life Sciences.