The son of the president of a machine tools company, Odegaard grew up on the north side of Chicago.
While neither parent had finished high school, they encouraged Odegaard's scholastic study and had an extensive library.
[citation needed] Odegaard taught history at the University of Illinois at Urbana-Champaign, and then took a leave of absence to serve in the Navy during World War II, earning the rank of lieutenant commander.
Odegaard returned to academia, first teaching at the University of Illinois, then becoming the Executive Director of the American Council Of Learned Societies.
The university witnessed tremendous growth during Odegaard's tenure with the student population growing from 16,000 to 34,000, 35 new buildings (doubling the square footage of the university), increased investment in the medical school, instituted a vision of building a "community of scholars", and oversaw the growth of the operating budget from $37 million USD in 1958 to over $400 million USD in 1973.