Moses graduated from Berea College in 1958 and from Vanderbilt University School of Medicine in 1962 with an MD. He completed his residency at Vanderbilt and did a postdoctoral fellowship at the National Institutes of Health. He then served as a faculty member at Vanderbilt for five years and then at the Mayo Clinic for twelve, where he was the chair of the department of cell biology.[1] He returned to Vanderbilt where he was the chair of cell biology and the founding director of the Vanderbilt Cancer Center. He stepped down as director in 2004.[1]