Born in Philadelphia, Neustadt received an A.B from UC Berkeley (1939), followed by an M.A degree from Harvard in 1941. After a short stint as an economist in the Office of Price Administration, he joined the U.S. Navy in 1942, where he was a supply officer in the Aleutian Islands, and stayed until 1946. He then went into the Bureau of Budget while working on his Harvard Ph.D, which he received in 1951.
He was the Special Assistant of the White House Office, from 1950 to 1953, under President Harry S. Truman. During the following year, he was a professor of public administration at Cornell, then from 1954 to 1964, taught government at Columbia, where he received a Woodrow Wilson Foundation Award (1961).
It was at Columbia that Neustadt wrote Presidential Power (1960; a revised edition entitled Presidential Power and the Modern Presidents: The Politics of Leadership appeared in 1990), in which he examined the decision-making process at the highest levels of government. He argued that the President is actually rather weak in the U.S. government, being unable to effect significant change without the approval of the Congress, and that in practice the President must rely on a combination of personal persuasion, professional reputation "inside the Beltway", and public prestige to get things done.
Appearing as it did just before the election of John F. Kennedy, Neustadt soon found himself in demand by the President-elect, and began his advisory role with a 20-page memo suggesting things the President should and should not try to do at the beginning of his term. During the 1960s Neustadt continued to advise both Kennedy and then Lyndon B. Johnson.
After his retirement he served as an advisor to Bill Clinton.