Born in Philadelphia, Neustadt received a BA in History from the University of California, Berkeley in 1939, followed by an M.A. degree from Harvard University 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 (now known as the Office of Management and Budget) while working on his Harvard Ph.D., which he received in 1951.

He was the Special Assistant of the White House Office from 1950-53 under President Harry S. Truman. During the following year, he was a professor of public administration at Cornell, then from 1954-64, taught government at Columbia University, where he received a Woodrow Wilson Foundation Award in 1961.

It was at Columbia that Neustadt wrote Presidential Power (1960; a revised edition titled 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.

With his book 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 Kennedy and later Lyndon B. Johnson.

Neustadt later founded the Kennedy School of Government at Harvard, where he taught as a popular professor for more than two decades, officially retiring in 1989, but continuing to teach there for years thereafter. Neustadt also served as the first director of the Harvard Institute of Politics (IOP), which was founded as "a living memorial to President John F. Kennedy that engages young people in politics and public service."

His first wife, Bertha Cummings "Bert" Neustadt, died in 1984; in 1987, he married British politician Shirley Williams, The Rt Hon. The Baroness Williams of Crosby, PC, who also served on the faculty at the Kennedy School of Government as Professor of Electoral Politics.

After his retirement he served as an advisor to Bill Clinton and as Chairman of the Presidential Debates Commission.

One of Neustadt's closest students was a young Al Gore. Gore's interest in politics was reignited by a junior seminar taught by Neustadt in 1968 on the presidency. In the course, Gore role-played John F. Kennedy during the Cuban Missile Crisis. Gore arranged to have private tutorials with Neustadt during his senior year, meeting with him two hours weekly.

Neustadt died in London after complications from a fall. In addition to Shirley Williams, Neustadt left a daughter, Beth, and a granddaughter. His son, Rick, predeceased him.