Kennedy was born on 22 October 1947 in Hythe, Kent, England. He spent a year 1965-6 studying at the Middle East Centre for Arab Studies at Shemlan in Lebanon; he had received a scholarship from the British Foreign Office. From 1966 to 1969, he studied at Pembroke College, Cambridge. He studied Arabic and Persian for Part 1 of the Tripos (achieving a 2:1), and history for Part II (achieving a first). He graduated from the University of Cambridge with a Bachelor of Arts (BA) degree in 1969. From 1969 to 1972, he was a postgraduate student within the Faculty of Oriental Studies, University of Cambridge. He completed his Doctor of Philosophy (PhD) degree in 1978 with a doctoral thesis titled Politics and the political élite in the early Abbasid Caliphate.
In 1972, Kennedy joined the University of St Andrews as a Lecturer in Mediaeval History. He was promoted to Reader in 1990. He was appointed Professor of Middle Eastern History in 1997. He held a number of academic administration appointments at St Andrews: he was Deputy Head of the School of History from 1992 to 1998, and was Dean of the Faculty of Arts from 1995 to 1998.
In 2007, he left the University of St Andrew's to join the School of Oriental and African Studies (SOAS), University of London. He was appointed Professor of Arabic at SOAS. From January 2015 to January 2018, he is leading a project at SOAS titled Economic integration and social change in the Islamic world system, 800-1000CE; it is being funded by the Leverhulme Trust.
Among his research topics is the History of the Islamic Middle East, Islamic Archaeology and Muslim Spain.