Educated at the Mackay School (Valparaíso, Chile) and the Grange School (Santiago, Chile), he completed a Bachelor of Science degree in the University of Florida and subsequently completed a Doctor of Philosophy in Economic History at the London School of Economics with a dissertation on "Arthur Young and the English Landed Interest".
His book The New World of the Gothic Fox points to factors such as the Spanish counter-reformation traditions and culture as an inhibitor of social innovation and economic development in Latin America in contrast to the successful development of British North America. Professor Véliz has also been a major critic of anti-colonialist historians such Manning Clark - a principal Australian historian. He considers Clark’s historical analysis as politically motivated and lacking an objective appreciation of the extension of Great Britain’s civilization into Australia.
Professor of Economic History, University of Chile, 1956–1960 Senior Research Fellow, Royal Institute of International Affairs, 1961–1966 Professor of International Politics, University of Chile, 1966–1972 Professor of International Politics, Chilean War Academy, 1968–1972 Professor of Sociology and Dean of the School of Social Sciences, Louisiana Trobe University, Melbourne, Australia (1972–1989) Visiting Professor of History, University of California, Los Angeles, 1969-1970.
Visiting Professor of History, Harvard University, 1979-1980. Professor of History and Director of the University Professors at Boston University (1990–2002).
Centralism, Nationalism, and Integration (1969).
Fellow Royal History Society. Member Sociedad de Bibliofilos Chilenos, Australian Institute International Affairs, Royal Society Victoria, Melbourne Club.
Married Maria Isabel Talavera Balmaceda. 6 children.