The son of a chemist, John Barrett Kelly initially attended University College, Auckland as a geology student before switching to history and literature. After teaching in schools in New Zealand, Queensland, England and Egypt, he took an MA and a Ph.D. at the London School of Economics. Kelly was a research fellow at the Institute of Colonial Studies at Oxford University from 1955 until 1958, and he served as an adviser to the Foreign Office on boundary disputes in the Arabian peninsula.

After leaving Oxford, Kelly taught at Wesleyan College, the University of Michigan, and the University of Wisconsin. In the 1980s he was a research fellow at the Woodrow Wilson Center and the Heritage Foundation in Washington, D.C., and he served as an adviser to the government of Oman in their border disputes with Saudi Arabia.