The Fred Hutchinson Cancer Research Center in Seattle, which Thomas joined in 1974, announced his death.
Thomas' work is among the greatest success stories in the treatment of cancer. Bone marrow transplantation and its sister therapy, blood stem cell transplantation, have improved the survival rates for patients with some blood cancers to around 90% from almost zero.
This year, about 60,000 transplants will be performed worldwide, according to the Hutchinson center.
"Imagine coming up with an idea, making it a reality and touching that many lives," said Dr. Fred Appelbaum, Thomas' friend and the director of the center's Clinical Research Division.
Thomas performed the first human bone marrow transplant in 1956. Along with a small team of fellow researchers, including his wife, Dottie, he pursued transplantations throughout the 1960s and 1970s despite skepticism from the medical establishment.
They sought to cure blood cancers by destroying a patient's diseased bone marrow with near-lethal doses of radiation and chemotherapy and then rescuing the patient by transplanting healthy marrow. The aim was to establish a functioning and cancer-free blood and immune system.
The procedure would go on to become the standard treatment for many sufferers of leukemia and lymphoma.
"He was brilliant, he was incredibly generous, and he was quick to deflect praise from himself to the individuals around him," Appelbaum said.
"At the same time, while he was quiet and modest, he was stubborn," he added. "He believed in what he was doing and he was going to make it happen. It's hard to imagine today how hard it was to make this reality because it was against the prevailing medical wisdom."
Edward Donnall Thomas was born in Mart, Texas, on March 15, 1920. His father was a doctor, the only general practitioner in their small town.
Thomas went to the University of Texas for his bachelor's and master's degrees, then received his medical degree from Harvard in 1946.
He spent two years in the Army, did research at the Massachusetts Institute of Technology and served his medical residency at Brigham Hospital in Boston. There he met Dr. Joseph E. Murray, who performed the first successful kidney transplant and who would share the Nobel Prize in 1990.
In 1955 Thomas moved to a hospital in Cooperstown, N.Y., where he performed the pioneering bone marrow transplant between identical twins.
Thomas joined the University of Washington faculty in 1963. In 1974, he became the first director of medical oncology at the Hutchinson center. It is now one of the world's top cancer treatment and research institutions.
Thomas also edited the first two editions of the bone marrow transplantations reference book, "Hematopoietic Cell Transplantation," which would become a bible for the field.
Thomas is survived by his wife of 70 years, two sons, a daughter, eight grandchildren and a great-grandchild.