Dr. Gleeson received his undergraduate and medical degrees from the University of Auckland (New Zealand). He completed his residency in Internal Medicine at the University of Auckland. In 1984 he came to the University of Utah as Chief Resident in Internal Medicine, and subsequently completed a fellowship in Endocrinology and Metabolism at the University of Utah.

He joined Lovelace Health Systems as an Endocrinologist in 1989. Lovelace Medical Group became ABQ Health Partners in 2007, and now is part of Optum Health. In the past he has served as Chief Quality Officer of Lovelace Health Systems, Chair of the Board of ABQ Health Partners, Medical Director of Medical Specialities and Primary care, as well as Medical Director for Risk Adjustment for the medical group. He continues to be active in multiple initiatives within the group, including serving on the national Value and Therapeutics committee.

Dr Gleeson is board certified in Internal Medicine, and Endocrinology and Metabolism. He is a Fellow of the Royal Australasian College of Physicians, a Fellow of the American College of Physicians, and a Fellow of the American College of Endocrinology. He is a clinical assistant professor of medicine in the University of New Mexico School of Medicine, is a past president of the Mountain States Region and the New Mexico affiliate of the American Diabetes Association, and past chair of the New Mexico Diabetes Advisory Council. He is a past president of the Greater Albuquerque Medical Association.