Rann completed a Bachelor of Arts and a Master of Arts (Political Studies) at the University of Auckland. While in New Zealand he was prominent in the campaign against French nuclear testing in the Pacific Ocean.
Rann was a political journalist for the New Zealand Broadcasting Corporation until 1977 when he moved to Adelaide and became press secretary and speech writer for then Premier Don Dunstan.
In 1985, he was elected to Parliament as the Member for Briggs and in December 1989 he became Minister for Employment and Further Education, Minister of Youth Affairs, Minister of Aboriginal Affairs and Minister assisting in Ethnic Affairs. After a cabinet reshuffle, Rann became Minister for Business and Regional Development, Minister of Tourism and Minister of State Services in September 1992.