Robert Finch was born in Tempe, Arizona, in 1925. He earned a bachelor's degree from Occidental College, Los Angeles, California in 1947 and his LL.B. from the University of Southern California in 1951.

After practicing law, Finch worked on Richard Nixon's unsuccessful presidential campaign in 1960. He later served the state of California as lieutenant governor from 1966 to 1969 under Governor Ronald Reagan. During the Nixon administration, Finch was secretary of health, education and welfare from 1969 to 1970.