He attended high school in Beaconsfield, Quebec and earned a B.Sc in biology from McGill University, Montreal, in 1976, a master of science degree in physiology, MD, and master of surgery degrees from McGill University, Montreal, in 1983. He completed a residency in family practice in the faculty of medicine, University of Ottawa, in 1985 and obtained fellowship in emergency medicine from the Royal College of Physicians and Surgeons of Canada, following completion of a residency in emergency medicine at the University of Toronto, in 1988.
His clinical research in emergency medicine has included studies evaluating the initial training and skill retention of cardiopulmonary resuscitation skills, patient survival from out-of-hospital cardiac arrest, the early identification of trauma patients at high risk, and the efficacy of tetanus immunization in the elderly.
In 1988 he became an emergency physician with the department of emergency services at Sunnybrook Health Science Centre as well as a lecturer with the Department of Surgery at the University of Toronto. He served as a member of the Air Ambulance Utilization Committee with the Ontario Ministry of Health both as an academic emergency physician and later as a representative of community emergency physicians. In addition, he has trained ambulance attendants, paramedics, nurses, residents, and practicing physicians in cardiac and trauma resuscitation as a course director in Advanced Cardiac Life Support (ACLS) with the Canadian Heart and Stroke Foundation and in Advanced Trauma Life Support with the American College of Surgeons.
From 1989 to 1990, he served as an emergency physician with the Emergency Associates of Kitchener-Waterloo and as Medical Director of the Westmount Urgent Care Clinic. In 1990 he returned to Sunnybrook as Medical Director of the ACLS program and coordinator of postgraduate training in emergency medicine. Subsequently, he became the Acting Director of the Department of Emergency Services at Sunnybrook Health Science Centre, Assistant Professor of Surgery, University of Toronto, and Assistant Professor of Medicine, University of Toronto. He remains active in life science and space medicine research, both as a Principal Investigator and as a Co-Investigator.
In April 2008, Williams was recruited by McMaster University as physician scientist where he is the director for the new McMaster Centre for Medical Robotics at St. Joseph's Hospital
Williams was mission specialist 3 on STS-90 Neurolab (April 17 to May 3, 1998). During the 16-day Spacelab flight, the seven-person crew aboard space shuttle Columbia served as both experiment subjects and operators for 26 individual life science experiments focusing on the effects of microgravity on the brain and nervous system. The STS-90 flight orbited the Earth 256 times, covered 6.3 million miles, and logged him over 381 hours in space.
From July 1998 to November 2002, Williams served as director of the space and life sciences directorate with responsibility for research in both physical and biomedical space sciences at JSC. Overall crew medical safety was one of his principal concerns, in addition to flight medical operations and JSC occupational and environmental health. His programs were directed toward protecting astronauts from the hazards of the space environment, including space radiation and microgravity, in addition to maintaining their medical, physical, and psychological well-being while aloft and on return to Earth. His other oversight responsibilities were in the fields of telemedicine, 3-D tissue culture/regeneration in microgravity, the curatorial management of extraterrestrial materials, and of qualifying humans for very long space journeys and ensuring their safe return to Earth.
Williams was assigned to the crew of STS-118, an assembly mission to the International Space Station. He completed three spacewalks during this mission, and set two new records during his final EVA on Saturday, 18 August: he is the Canadian with the most spacewalks (3); and he passed Canadian Astronaut Chris Hadfield in total EVA time. Williams ended Saturday's EVA with a total of 17 hours, 47 minutes of extravehicular time. He was the second Canadian to lead an EVA, after Chris Hadfield, who led an EVA during STS-100.
Williams was awarded the Commonwealth Certificate of Thanks in 1973 and the Commonwealth Recognition Award (1975) for his contribution to the Royal Life Saving Society of Canada. Academic awards include the A.S. Hill Bursary, McGill University, in 1980; the Walter Hoare Bursary, McGill University, in 1981; and the J.W. McConnell Award, McGill University, from 1981 to 1983. He was named Faculty Scholar in 1982 and University Scholar in 1983 by the faculty of medicine at McGill University. In 1983, he also received the psychiatry prize and the Wood Gold Medal from the Faculty of Medicine and was named on the dean's honor list by the physiology department, at McGill University, for his postgraduate research. He was twice awarded the second prize for his participation in the University of Toronto Emergency Medicine Research Papers Program, in 1986 and 1988, and received top honors in that competition in 1987.