Adrian John Bickersteth Wood was born on January 25, 1946 in Woking, England. He graduated from Cambridge University (BA) in 1967 and received a Masters in Public Administration (MPA) from Harvard University in 1969. He returned to Cambridge, completing his PhD in 1973, while working as a Fellow of King's College, Cambridge from 1969 to 1977. He was also a lecturer in the Economics Faculty of Cambridge University from 1973 to 1977.

Wood joined the World Bank in 1977 as an economist in the Europe, Middle East, and North Africa Regional Vice Presidency (EMENA), working on Turkey until 1979, when he was recruited to the core team that prepared the 1980 World Development Report. In 1980, he became an economist in the new China Division in the East Asia and Pacific Regional Vice Presidency (AENVP), at a major transition point when the People's Republic of China had assumed representation as China in the World Bank Group in May of that year. Wood remained in the China Division until he left the Bank in 1985.

From 1985 to 2000, Wood was a professorial fellow of the Institute of Development Studies (IDS) at the University of Sussex in the UK. During this time, he continued to work on China as a Bank consultant, primarily on state-owned enterprises. From 2000 to 2005, he was chief economist of the United Kingdom's Department for International Development (DFID), and from 2005 to 2011 was professor of International Development at the University of Oxford.

After leaving the Bank, Wood did further work on China as a Bank consultant. He was involved with DFID's work in China, including the establishment in 2017 of China's Centre for International Knowledge on Development. At Oxford, he worked under the auspices of the Cairncross Foundation (with former Bank colleagues including Edwin Lim and Gene Tidrick) on advisory reports for China.