Gullstrand married Signe Breitholtz (1862–1946) in 1885 and died in Stockholm, where he was interred at Norra begravningsplatsen.
Born at Landskrona, Sweden, Gullstrand was professor (1894–1927) successively of eye therapy and of optics at the University of Uppsala. He applied the methods of physical mathematics to the study of optical images and of the refraction of light in the eye. For this work, he received the Nobel Prize in Physiology or Medicine in 1911.
He was elected a member of the Royal Swedish Academy of Sciences in 1905, and served on the Academy's Prize Committee for Physics. While serving on the committee, he used his position to block Einstein from receiving a Nobel Prize in Physics for his theory of relativity, which Allvar believed to be wrong.