Wegman, a St. Louis, Missouri native, received a B.S. in mathematics from Saint Louis University in 1965. He then went to graduate school at the University of Iowa, where he earned an M.S. in 1967 and a Ph.D. in 1968, both in mathematical statistics. He held a faculty position at the University of North Carolina for ten years. In 1978, Wegman joined the Office of Naval Research, in which he headed the Mathematical Sciences Division. Later, Wegman served as the first program director of the Ultra High Speed Computing basic research program for the Strategic Defense Initiative's Innovative Science and Technology Office. He joined the faculty of George Mason University in 1986 and developed a master’s degree program in statistical science.
Wegman is credited with coining the phrase "computational statistics" and developing a high-profile research program around the concept that computing resources could transform statistical techniques. He also has been the associate editor of seven academic journals, a member of numerous editorial boards, and the author of more than 160 papers and five books. Wegman is a member of the American Statistical Association, a former president of the International Association for Statistical Computing, and a past chairman of the Committee on Applied and Theoretical Statistics for the United States National Academy of Sciences. Wegman received the 2002 Founders Award from the American Statistical Association for "over thirty years of exceptional service and leadership to the American Statistical Association."
In 2006, Republican Congressman Joe Barton chose Wegman to assist the House Energy and Commerce Committee in its inquiry criticizing the multi-proxy paleoclimate reconstructions which had been dubbed the "Hockey stick graph". Wegman produced a report and offered testimony supporting published papers disputing the methodology and data used by the climate scientists. The legitimacy of this investigation was disputed, and Sherwood Boehlert as chairman of the United States House Committee on Science, Space and Technology arranged for an investigation by the National Research Council, the North Report which found that the Wegman committee's conclusions lacked substance.