Boodberg came from a Baltic German family that had lived in Estonia for centuries. They traced their origins to 1006, to German emigrants from Mainz to Estonia in the thirteenth century. After Russia annexed Estonia in 1721, they became a prominent diplomatic and military family in Imperial Russia.
Boodberg was born in Vladivostok, where his father was commanding general of the Russian forces. At the outbreak of World War One, he was a cadet at a military school in St. Petersburg. In 1915, he and his brother were sent for safety to Harbin in Manchuria, where he began the study of philology. From there, he went to the Oriental Institute in Vladivostok and studied Chinese. In the summer of 1920, he left Russia and moved to San Francisco, where his family soon joined him; he enrolled in the University of California, Berkeley, getting a B.A. in Oriental Languages in 1924 and a Ph.D. in 1930. In 1932, Berkeley hired him as an Instructor in Oriental Languages; he became an Associate Professor in 1937, Chairman of the department in 1940, and Full Professor in 1948, winning Guggenheim Fellowships in 1938, 1956, and 1963, in the latter year becoming President of the American Oriental Society. He continued to teach until his death (of a heart attack) in 1972, influencing several generations of sinologists, notably Edward H. Schafer, who wrote a long obituary article in the Journal of the American Oriental Society that was followed by a full bibliography by Alvin P. Cohen.