Finch served in the Marine Corps in World War II. After the war, he served Congressman Norris Poulson as an aide, and befriended a novice Washington politician named Richard Nixon. He returned to Southern California to study law at the University of Southern California. He served again as a Marine during the Korean War. He then practiced law for a few years before returning to Washington as Vice President Nixon's aide. He later served as manager of Nixon's unsuccessful 1960 presidential campaign against John F. Kennedy.
In 1966 Finch was elected Lieutenant Governor of California, receiving more votes than Ronald Reagan, who was elected Governor in the same election. During 1968, he was a senior advisor in Richard Nixon's presidential campaign, and when Nixon became President, Finch joined the new Administration in 1969 as Secretary of Health, Education and Welfare. In 1970, Finch left HEW for the White House staff, where he served two years as Counsellor to the President and continued as a member of the Cabinet. After resigning from the White House in 1973, Finch returned to Southern California, where he practiced law in Pasadena and remained engaged in Republican politics until his death. He was an unsuccessful candidate for the Republican nomination for U.S. Senate in 1976, losing to S.I. Hayakawa who went on to win the general election.
During the 1968 presidential election, Finch was Nixon's first choice as his Vice Presidential running mate , but Finch declined and Nixon then chose Governor of Maryland Spiro Agnew. Nixon-Finch ticket was possible because, although Nixon was born and represented California in Congress, during 1968 election he was a resident of New York and California's electors would be preemited to cast their vote on both (if they were both California's residents at time, California's electors would be unable to vote for both of them).
Following Nixon's election, Finch was given his choice in the new Cabinet, and he selected Secretary of HEW because of his long interest in health and education issues. Finch was more moderate than Nixon, especially in social issues, but political differences never affected their long and close relationship, with the two staying in contact until Nixon's death in 1994.