Thomas was born at Mart in Texas and educated at the University of Texas, receiving his BA in 1941 and MA two years later. In 1946 he was awarded his MD by Harvard University. He worked at the Peter Bent Brigham Hospital, Boston, from 1946, eventually specializing in hematology. After two years as a research associate with the Cancer Research Foundation at the Children's Medical Center, Boston (1953–55), he moved to the Mary Imogene Bassett Hospital as hematologist and assistant physician. In 1956 he became associate clinical professor of medicine at the College of Physicians and Surgeons, Columbia University, and from 1963 until 1990 he served with the University of Washington Medical School in Seattle as professor of medicine.

Although primarily a clinician rather than a research scientist, Thomas was instrumental in gaining new insights into how the body's immune system rejects tissue transplants. His expertise in hematology and cancer biology enabled him to develop the technique of bone-marrow transplantation to treat patients suffering from leukemia or other cancers of the blood. This involves the transfer of bone-marrow cells from a healthy donor to the bone marrow of the patient, so that the patient can resume production of healthy white blood cells to replace the cancerous cells.

In experiments using dogs, Thomas demonstrated the importance of matching donor tissue and the recipient's tissue as closely as possible, so as to minimize the risk of rejection of the transplanted tissue. He also showed that by treating the recipient with cell-killing drugs, it was possible to avoid another of the pitfalls associated with tissue transplantation, namely, the graft-versus-host reaction. This occurs when immune cells belonging to the donor and transferred with the transplant recognize the host's tissues as foreign and start to attack them.

Under Thomas's leadership the University of Washington Medical School became the preeminent North American center for bone-marrow transplants, where physicians from all over the world came to learn the technique. For his work Thomas was awarded the 1990 Nobel Prize for physiology or medicine, jointly with Joseph Murray.