Born in Dundee, the son of an ophthalmologist, and educated at Lathallan School in Fife, Moodie contracted polio at the age of nine (which left him with a lifelong limp) and was taught in hospital until 1936.
While studying at The Queen's College, Oxford, he was elected president of the Junior Common Room and the University Liberal Club.
He pursued his interest in politics outside academia, standing as the Labour Party candidate for Dumfriesshire in the 1959 general election, and gathering 42% of the vote.
Moodie became the first professor of politics and head of department at the newly founded University of York in 1963, where he remained until his retirement in 1980.
During this time, he helped to establish the university's Centre for Southern African Studies, and continued work in this field after his retirement, researching post-apartheid academia and particularly academic freedom.