[3] Murray shared the Nobel Prize in Physiology or Medicine in 1990 with E. Donnall Thomas for "their discoveries concerning organ and cell transplantation in the treatment of human disease.

His unit cared for thousands of soldiers wounded on the battlefields of World War II, working to reconstruct their disfigured hands and faces.

The donor grafts survived long enough for Woods’ own healthy skin to be harvested and used as autografts to cover the burned areas.

Many of his peers discounted his pursuit, believing that the problem of immune rejection was insurmountable,[9] as French surgeon Alexis Carrel (1873–1944), a 1912 Nobel Prize laureate, had concluded from his research that a “biological force” would forever prevent successful transplantation.

During preparations for the first transplant surgery, Murray and his team consulted clergy of all denominations while weighing the ethical issues of the procedure.

In Operating Room 2 of the Peter Bent Brigham Hospital, Murray transplanted a healthy kidney donated by Ronald Herrick into his twin brother Richard, who was dying of chronic nephritis.

In 1959, Murray went on to perform the world's first successful allograft, who received a kidney from his non-identical brother, after being treated with total body irradiation and continued to live for another 28 years.

in 1960, Murray had to get the approval of the Massachusetts Superior courtl before being able to transplant a kidney for a family who travelled from Red Deer, Alberta, Canada to see Dr. Murray from 12-year-old Lana Nightingale into her twin sister Johanna, who became the longest surviving kidney-transplant recipient with over 50 years, which is still the World Guinness Record for longest surviving kidney transplant patient.

In 1962, Dr. Murray performed the first successful deceased donor (cadaveric) kidney transplant treated with Imuran, a derivate of 6-MP and steroids.

In 1967, he participated in defining brain death, when Robert Ebert, the Dean of the Harvard Medical School convened a group of physicians, ethicists, and legal scholars to examine the characteristics of a permanently nonfunctioning brain, and Dr Murray was a member of that committee, which included famed neurosurgeon William Sweet, neurologist Raymond Adams, and legal scholar William J. Curran.

[18] In 1990, he was honored with the Nobel Prize in Physiology or Medicine for his pioneering work in organ transplantation, together with hematologist E. Donnall Thomas.

Murray was selected to receive the Laetare Medal by the University of Notre Dame in recognition of outstanding service to the Catholic Church and society in March 2005.

[21] Joseph Murray married his college life sweetheart Virginia (Bobby) née Link in June 1945, the two having first met at the Boston Symphony Orchestra, with whom he would have 6 children: 3 boys and 3 girls.