Rosser has served as President of California State University, Los Angeles since 1979, and he is also Professor of Health Care Management. He earned academic degrees in health education and microbiology from Southern Illinois University at Carbondale. He held the post of researcher at the Eli Lilly & Company Research Laboratories in Indianapolis, Indiana, from 1963 to 1966. He has served as consultant to the National Institutes of Health's National Heart and Lung Institute, member of the New Jersey Board of Medical Examiners, and member of the National Advisory Council on Aging through the National Institutes of Health and the National Health Foundation. Rosser has published works on health issues and the health profession, and has also written or edited a wide variety of works in the field of higher education administration.

Dr. Rosser's honors include the Southern Illinois University Alumni Achievement Award; the Golden State Minority Foundation's 1990 Medal of Excellence; and the National Science Foundation's Educator Achievement Award.