A native of Chicago, Young became interested in native American languages when he discovered that a group of Mexican farmworkers whom he encountered spoke, in addition to Spanish, Nahuatl. After earning a liberal arts degree from the University of Illinois in 1935, he moved to New Mexico where he enrolled in graduate school in Anthropology at the University of New Mexico and began his study of Navajo.
In the early 1940s he joined the Bureau of Indian Affairs where he worked primarily on programs related to Navajo language and education. This work was interrupted by a stint in the Marine Corps during the Second World War, during which he was involved in the Navajo Code Talker project. Upon his retirement from the Bureau of Indian Affairs in 1971 he became an adjunct professor of Linguistics at the University of New Mexico.
In July 1996, Robert Young was honored, along with William Morgan, in the Navajo Nation Council Chambers for his work on the Navajo language. The two were presented Pendleton Blankets embroidered with the seal of the Navajo Nation.