Angel completed his undergraduate degree at Harvard College in 1936 where he studied under Clyde Kluckhohn, Carleton S. Coon and Earnest A. Hooton.
Hooton had a particular influence on Angel and arranged for him to conduct field work in Greece early in his career as a graduate student.
In 1943 he accepted a post in the anatomy department of Jefferson Medical College in Philadelphia, Pennsylvania where he taught and conducted research until his appointment in 1962 as Curator of Physical (Biological) Anthropology at the National Museum of Natural History, Smithsonian Institution.
He was a consultant to the Federal Bureau of Investigation but also assisted many regional police units in identifying human remains from forensic cases.
He worked closely with archaeologists in his effort to reconstruct what he called the social biology of archaeological human populations.