Following high school, Peterson attended Dartmouth College, where he graduated in 1960. He received his M.D. from the University of Washington in 1964, then moved to New York for his internship and residency at Bellevue and Memorial Sloan-Kettering Hospitals. He received his Board Certification in both Internal Medicine and Cardiovascular Disease.

John returned to Seattle, to the University of Washington, in 1970. In 1972, he began a long and honored affiliation with Swedish Hospital, where he has since served as Director of the Cardiac Catheterization Laboratory and as Chief of the Department of Cardiology. Although he retired from practice at the end of December 2014, he still serves on the Board of Governors of the Swedish Medical Center Foundation.

In the course of his career, among other honors, John has been recognized by his peers as a Fellow of the American College of Physicians, the Council on Clinical Cardiology of the American Heart Association, and the American College of Cardiology. He served as chairman of the scientific sessions for the Washington State Medical Society Annual Meetings in 1983 and 1984. He sat on the Board of Directors of the American Heart Association of Washington, and served as Chairman of its Professional Education Committee for many years, as Chairman of the Annual Meeting in 1983, and as President of its King County Metro Division for 1993-1994.