"Dr. Bill", as he's known to his patients, graduated from Northwestern University Medical School. Following an Internship at Cleveland Metropolitan General Hospital, Dr. Stuart returned to Northwestern University where he completed an Internal Medicine Residency. He subsequently served as an Epidemic Intelligence Service Officer at the Communicable Disease Center in Atlanta for two years following which he completed a three-year Fellowship in Neurology at Emory University Medical School. Upon completion of this training and serving at the NINDS he entered private practice in the Atlanta area, forming the Atlanta Neurological Clinic, subsequently renamed The Peachtree Neurological Clinic. Dr. Stuart was one of the founding members of the American Society of Neuroimaging and he has remained active with this organization since he served as its president in 1984 and 1985.

He has served as a member of the Executive Committee of the American Academy of Neurology and served for 2 years as the Treasurer. He was twice named the Clinical Teacher of the Year at Piedmont Hospital. He began his focused interest in Multiple Sclerosis in 1988, developing the Multiple Sclerosis Comprehensive Care and Research Center at Shepherd Center in 1991. In January 2001, he founded the Multiple Sclerosis Center of Atlanta.