Born in Brooklyn, New York, he graduated from Columbia University and married Hannah Geffen in 1920. They lived in Europe in the 1920s.

Initially Josephson wrote poetry, published in Galimathias (1923), and reported for various "little magazines." He became associate editor of Broom (1922-24) and contributing editor of Transition (1928-29). Josephson was also a regular contributor to The New Republic, The Nation, The New Yorker, and the Saturday Evening Post.

Josephson's first biographies were Zola and His Time (1928) and Jean-Jacques Rousseau (1932). Influenced by Charles A. Beard and the Depression, and with only one major exception, Stendhal: or the Pursuit of Happiness (1946), Josephson changed his focus of interest from literature to economic history when he published The Robber Barons in 1934. This was followed by more full-length works in which Josephson served as a spokesman for intellectuals of his generation who were dissatisfied with the social and political status quo.

Josephson wrote two memoirs, Life Among the Surrealists (1962) and Infidel in the Temple (1967). In 1978, he died in Santa Cruz, California. He was 79.

Josephson's collected papers are in the Yale Collection of American Literature, Beinecke Rare Book and Manuscript Library at Yale University.

Hannah Josephson, librarian of the American Academy of Arts and Letters and an author in her own right, worked closely with her husband on various projects throughout their careers. In 1945 she and Malcolm Cowley edited Aragon, Poet of the Resistance. Matthew and Hannah Josephson collaborated on Al Smith: Hero of the Cities in 1969. They had two sons, Eric and Carl.

Josephson is also credited with popularizing the term "robber baron" in one of his books.

• Galimathias (1923)
• Zola and His Time (1928, biography)
• Portrait of the Artist as American (1930)
• Jean-Jacques Rousseau (1932, biography)
• The Politicos (1938, essay)
• The President Makers: The Culture of Politics and Leadership in an Age of Enlightenment 1896-1919 (1940)
• Victor Hugo (1942, biography)
• Empire of the Air: Juan Trippe and the Struggle for World Airways (1943)
• Stendhal (1946, biography)
• Sidney Hillman (1952, biography)
• Edison (1959, biography)
• Life Among the Surrealists (1962, memoir)
• Infidel in the Temple: a memoir of the 1930s (1967, memoir)
• The Money Lords, The Great Finance Capitalists, 1925-1950 (1972, nonfiction)
• Al Smith: Hero of the Cities; a Political Portrait Drawing on the Papers of Frances Perkins (1969)

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• Union House Union Bar: The History of the Hotel & Restaurant Employees and Bartenders International Union, AFL-CIO