Born in Scotland, Wilson was educated in Trinity College, Glenalmond, Keble College, Oxford, and London University (PhD in contemporary history, (1955-1958), Master of Arts). He studied the Chinese language from 1960 to 1962 in Hong Kong while he worked as the Political advisor for the Governor of Hong Kong, named in Chinese as 魏德維, and 1963-1965 in Beijing. His original Chinese name before the governorship was Wèi Déwéi (魏德巍 Jyutping: Ngai6 Dak1-ngai4); then he changed it to Wèi Yìxìn (衛奕信 Wai6 Jik6-seon3) to better transcribe his family name in Cantonese.
From 1977 to 1981, Wilson was a consultant of the governor of Hong Kong. Then he was a diplomat to southern Europe. In 1984, he worked on diplomatic matters with Asia-Pacific. He was a British delegate in the Sino-British Joint Liaison Group (中英聯合聯絡小組) in 1984.
As a governor, Wilson encountered the Vietnamese boat refugees problem. He proposed the building of an airport on Lantau Island, known as the "Rose Garden Project" (「玫瑰園計劃」, see Hong Kong International Airport). He retired before the end of his term. In addition, Wilson made possible the eighteen legislators of the Legislative Council directly elected by Hongkongers.
After his governorship, he became the chairman of the utility company Scottish Hydro Electric plc (later Scottish and Southern Energy) in Perth, Scotland between 1993 and 2000.
He was appointed a Vice-President of the Royal Scottish Geographical Society (1996) and Chancellor of the University of Aberdeen (1997).
The 78-kilometre Wilson Tail (衛奕信徑), containing ten hiking segments aligned north-south in Hong Kong, is named after him. As is the Lord Wilson Heritage Trust (衛奕信勳爵文物信託) based in Wanchai, established in December 1992 to preserve Hong Kong's historical culture.
Wilson lives in Edinburgh, has been married to Natasha Helen Mary since 1967.