He was born to an orthodox Brahmin family in Srikakulam, Andhra Pradesh, South India to V. Gumpaswami and V. Sundaramma. His father was a government servant. The greatest single influence on Rama was that of his paternal grandfather, Vulimiri Ramalingaswami, after whom he was named. His grandfather carried the honorific title of ‘Pantulu Gaaru’ which in Telugu means ‘respected teacher’. He was a scholar of Sanskrit, Telugu, and English, and was a graduate in English literature from Madras University. A staunch nationalist who did not want to serve under an alien government, his grandfather chose to be headmaster of a high school started by the Raja of Bobbili, which he developed into the best school in the Andhra Pradesh of that time. He received his medical education from Andhra Medical College, Vishakapatnam and then went on a scholarship to Oxford. His pioneering research on nutrition got him elected to the National Academy of Sciences, Russian Academy of Medical Sciences and the Royal Society of London. He was also the director of All India Institute of Medical Sciences and later on director general of Indian Council of Medical Research and President of the Indian National Science Academy.
He was regarded a teacher of international repute in the areas of nutritional deficiency.He became the Director of the institute and served the premier institute for 10 years 1969-1979). He became the Director General of Indian Council of Medical Research, New Delhi. In remembrance of his great service, the Indian Government has decided to name the Indian Council of Medical Research building after him (Ramalingaswami Bhavan). He was also President of the Indian National Science Academy. He was Special Advisor to World Health Organization and President of National Institute of Immunology. He has served as Chair of the International Task Force on Health Research for Development in Geneva (1990–93). He was Secretary-General of the International Conference on Nutrition, in Rome in December 1992, which was held under the auspices of the World Health Organization and the Food and Agriculture Organization of the United Nations. He was appointed to the Board of Governors of the International Development Research Centre (IDRC), Canada in 1999. His contributions to pathophysiology of protein energy malnutrition are well known. His classical experiments on correction of Iodine deficiency by supplementation of common salt with potassium iodate laid foundation for the National Iodine Deficiency Control Programme. He has significant contributions in the discovery of new syndrome of Non-cirrhotic Portal Fibrosis (NCPF) and Indian Childhood Cirrhosis. He has been honored with Shanti Swarup Bhatnagar Award by Council of Scientific and Industrial Research in 1967 and Padma Shri in 1969, Padma Bhushan and Padma Vibhushan by Government of India, KK Birla National Award, and Basanti Devi Amirchand Prize (ICMR) in 1966. Leon Bernard Foundation Award was presented to him by Sir Harold Walter, president of the 1976 World Health Assembly.