Goodwin was born in Boston, Massachusetts. He attended Brookline High School and graduated summa cum laude from Tufts University in 1953. He went on to study at Harvard Law School, graduated summa cum laude in 1958 and joined the Massachusetts State bar the same year. He was married to Sandra Leverant from June 15, 1958 until her death in 1972. After clerking for United States Supreme Court Justice Felix Frankfurter in 1958, Goodwin came to Senator John F. Kennedy's attention in 1959 while working as special counsel to the Legislative Oversight Subcommittee of the U.S. House of Representatives, where Goodwin was involved in investigating the Twenty One quiz show scandal (which provided the story for the 1994 movie Quiz Show in which he is portrayed by actor Rob Morrow).
Goodwin joined Kennedy's speech writing staff in 1959, and after Kennedy's successful presidential bid, served as assistant special counsel to the President in 1961. Goodwin was also a member of Kennedy's Task Force on Latin American Affairs and in 1961, was appointed Deputy Assistant Secretary of State for Inter-American Affairs, a position he held until 1963. As one of Kennedy's specialists in Latin-American affairs, Goodwin helped develop the Alliance for Progress, an economic development program for Latin America, and met secretly with Che Guevara in Uruguay in August 1961. From 1963 to 1964, Goodwin served as secretary-general of the International Peace Corps and in 1964 became special assistant to President Lyndon B. Johnson. He has been credited with naming Johnson's legislative agenda "the Great Society".
Goodwin left government service in 1965, though returned briefly in 1968 to write speeches for presidential candidates Robert F. Kennedy, Eugene McCarthy and Edmund Muskie. After leaving government, Goodwin served as a Fellow on the faculty in the Center for Advanced Studies at Wesleyan University in Middletown, Connecticut from 1965 to 1967 and as a visiting professor of public affairs at the Massachusetts Institute of Technology in 1968. After Senator Kennedy's death he retired from politics and became a writer.
Along with acting as a contributor to Rolling Stone and The New Yorker, Goodwin has published numerous books, articles and plays. In 2003, the Yvonne Arnaud Theatre in Guildford, England produced his new work The Hinge of the World, which took as its subject matter the quarrel between Galileo Galilei and the Vatican. Retitled Two Men of Florence (referring to Galileo and his adversary Pope Urban VIII, who as Cardinal Maffeo Barberini had once been Galileo's mentor), the play made its American debut at the Huntington Theatre in Boston in March 2009.
In 1975, Goodwin married Doris Kearns Goodwin, with whom he reared three children: Richard, Michael, and Joseph.