Skegg was born in Auckland and attended King's College, Auckland. He entered the medical course at the University of Otago, travelling on exchange to Harvard University. He later received a (postgraduate) Rhodes Scholarship to the University of Oxford, joining Balliol College and working with noted epidemiologist Sir Richard Doll.
Returning to Otago, Skegg took up the departmental chair in Preventive and Social Medicine in 1980. In 2004, he took up the Vice-Chancellorship of the university. He stood down from that position in 2011. He was appointed President of the Royal Society of New Zealand in July 2012.
Skegg has acted as a consultant to the World Health Organization and to the New Zealand government. He chaired the Health Research Council, the Science Board, and the Public Health Commission. In 1990, he was appointed an OBE for services to medicine and, in the 2009 New Year Honours, he was appointed a Distinguished Companion of the New Zealand Order of Merit, also for services to medicine. Later in 2009, he accepted re-designation as a Knight Companion following the restoration of titular honours by the New Zealand government. He has contributed to the study of cervical, breast and prostate cancer, as well as contraceptives and reproductive health.
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