Rosset was born and raised in Chicago to a Jewish father, Barnet Rosset, and an Irish Catholic mother, Mary (née Tansey). He attended the progressive Francis Parker School, where he was best friends with renowned cinematographer Haskell Wexler. He went on to study at Swarthmore College, UCLA and the New School for Social Research. He was graduated from the University of Chicago and received a second degree from the New School. During World War II, he served in the Army Signal Corps as an officer in a photographic company stationed in China. Rosset married American Abstract Expressionist painter Joan Mitchell in 1949. The couple later divorced. Mitchell was instrumental in Rosset’s acquisition of Grove Press. He owned an East Hampton Long Island quonset hut, previously used as a studio by painter Robert Motherwell.

Rosset introduced American readers to numerous significant writers, including Samuel Beckett (Nobel Prize in Literature 1969), Pablo Neruda (Nobel Prize 1971), Octavio Paz (Nobel Prize 1990), Kenzaburō Ōe (Nobel Prize 1994), Harold Pinter (Nobel Prize 2005), Henry Miller, William S. Burroughs, Khushwant Singh, Jean Genet, John Rechy, Eugène Ionesco and Tom Stoppard.  Launched in 1957, Evergreen Review pushed the limits of censorship, inspiring hundreds of thousands of younger Americans[citation needed] to embrace the counterculture. Grove Press published Beat Generation writers, including William Burroughs, Allen Ginsberg, Lawrence Ferlinghetti, John Rechy, Hubert Selby, Jr. and Jack Kerouac. Rosset also purchased the American distribution rights to the Swedish film I Am Curious (Yellow).  The online Evergreen Review features Beat classics as well as debuts of contemporary writers, including Giannina Braschi and Dennis Nurkse. In 2007, Rossett married Astrid Myers, managing editor of the online Evergreen Review. In 2008, Rosset completed writing his autobiography. He died in 2012 after a double heart valve replacement.