After completing his graduate education with master's and doctoral degrees at Harvard University, Kelly had a career spanning academic service, and professional excavations under the Smithsonian Institution and other organizations.
In 1947 he was selected by University of Georgia to be founding chairman of a Department of Anthropology there, serving in that role until 1963, followed by several years as a professor.
While there he also worked on the Cahokia Mound site, the center of the Mississippian culture that influenced much of North America through the Ohio and Mississippi waterways and trade routes.
This was being explored as a part of the Federal relief archaeological program, which provided jobs to workers to help excavate the sites.
In 1939 Kelly was promoted to chief archaeologist of the National Park Service, and served at NPS headquarters in Washington, D.C.
Kelly and his wife, Rowana, had four daughters together: Sheila, Joanna, Patricia, and Cora Lewis.