He was born and raised in Cambridge, Massachusetts to Henry Bradford Washburn, Sr., dean of the Episcopal Theological School in Cambridge, and Edith Buckingham Hall. He was the younger brother of Henry Bradford Washburn. In his youth, Washburn took a keen interest in the field of natural history, and during school vacations worked with exhibits and collections in Harvard’s Museum of Comparative Zoology. Washburn graduated summa cum laude from Harvard University with a bachelor's degree in Anthropology in 1935, followed by a Ph.D. in Anthropology in 1940. For a time, Washburn considered pursuing his doctorate in zoology, and in his first year in graduate school, worked as an assistant with a zoological expedition in southern Asia called the Asiatic Primate Expedition. His work as a graduate student in comparative anatomy, comparative psychology, animal locomotion mechanics, and paleontology helped shape in him a multi-disciplinary perspective toward the study of evolutionary origins. Washburn married Henrietta Pease in 1938, and they had two children, Sherwood "Tuck" and Stan. They subsequently resided in New York, Chicago, Illinois and Berkeley, California, where Sherwood held university positions. Washburn died in Berkeley in 2000 at age 88.
Harvard
Washburn entered Harvard's graduate program with the intention of pursuing a doctorate in zoology. His focus shifted to anthropology after being induced to attend an introductory seminar on the subject led by his freshman advisor and close family friend Alfred Tozzer. Finding the mixture of archaeology, customs and human evolution stimulating, he joined the physical anthropology program led by Earnest Hooton where he was able to enfold his zoological coursework such as comparative anatomy and paleontology in his approach to the study of human evolution. Doctoral students in Harvard's physical anthropology program were forced to look beyond the anthropology department to secure the necessary training, which Washburn considered fortuitous because the experience left him with deep appreciation how much more can be learned when a multidisciplinary effort is brought into the analysis. While studying for his doctorate, Washburn received his first opportunity to engage in fieldwork. He served as an assistant zoologist in Harold J. Coolidge's 1935–1936 Asiatic Primate Expedition. In Malaysia he helped collect specimens of various species of colobine and macaque monkeys and the orangutan. In Sri Lanka and Thailand he also collected specimens of lar gibbon and observed their behavior in natural surroundings. He continued this work on the collection when he returned to Harvard, at times assisted by Gabriel Lasker. Washburn would later credit the ongoing discussions between Lasker and himself during this period as formative to his views about human variability. To Washburn, human variability was to be understood in terms of population genetics, and not according to the terms of racial and constitutional typology as typified by his doctoral advisor, Hooton. His doctoral thesis was a metrical appraisal of proportions in the skeletons of adult macaques and langurs. His doctorate, awarded in 1940, was the first from Harvard's anthropology department to be awarded for a study of non-human primates.