Becoming a radiologist requires the completion of an undergraduate education, medical school, a year of internship, and four years of clinical residency. For those intending to practice a subspecialty like neuroradiology or pediatric radiology, the residency is followed by a few years of specialized fellowship training.t takes at least 13 years of postsecondary education and clinical training to become a diagnostic radiologist. That includes a 4-year bachelor education, 4 years of medical school, a year-long internship, and 4 years of residency.