Mills was born in Englewood, New Jersey, and graduated from George School. He studied at Columbia College, 1944-1948, while on leave from the Coast Guard. Mills demonstrated his mathematical ability by winning the Putnam national mathematics contest in 1948, and by receiving first-class honors in the Tripos. He earned a master's degree from Cambridge, and a Ph.D.in Physics under Norman Kroll, from Columbia in 1955. After a year at the Institute for Advanced Study in Princeton, New Jersey, Mills was a professor of Physics at Ohio State University from 1956 to his retirement in 1995.

Mills and Yang shared the 1980 Rumford Premium Prize from the American Academy of Arts and Sciences for their "development of a generalized gauge invariant field theory" in 1954.