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. Rosset also said that Robert Morss Lovett, the grandfather of Rosset's high school sweetheart, and professor of English at the University of Chicago had been a great influence on him.
Rosset attended Swarthmore College for one year and then enlisted in the army in 1942. It was at Swarthmore that Rosset discovered the work of Henry Miller.
During World War II, he served in the Army Signal Corps as an officer in a photographic company stationed in Kumming, China. In 2002, Rosset exhibited a collection of his War Photographs from his time in China in a New York Gallery. The exhibit included graphic photos of wounded and dead Chiang Kai-shek soldiers.
Rosset's initial ambition was to be a filmmaker like his childhood friend Haskell Wexler. Rosset produced a documentary called Strange Victory about racism in a post World War II America. The film was a failure.
After divorcing his first wife, painter Joan Mitchell, Rosset took courses at the New School for Social Research and worked for Monthly Review Press magazine. A friend of Joan Mitchell's told Rossett about Grove Press and that the original founders wanted to sell. Rossett purchased Grove Press for three thousand dollars.
Rosset married five times. Rosset married American Abstract Expressionist painter Joan Mitchell in France in 1949. The couple settled in Greenwich Village but then later divorced. Mitchell was instrumental in Rosset's acquisition of Grove Press.
Rosset's second wife was Loly Eckert, a sales manager at Grove Press. They had a son named Peter Rosset.
He owned an East Hampton, Long Island quonset hut, previously used as a studio by painter Robert Motherwell.
His final marriage was to Astrid Meyers.
Rosset had three more children after Peter, son Beckett (named for Samuel Beckett) and two daughters—Tansey and Chantal.
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.
Interviewed by Tin House publisher Win McCormack, Rosset talked about publishing Beckett:
I had actually read a little bit of Beckett in transition
Magazine and a couple of other places. I was going to the New School. My New School life and the beginnings of Grove crossed over. At the New School, I had professors like Wallace Fowlie, Alfred Kazin, Stanley Kunitz and others, who were very, very important to me. I was doing a great deal of reading and writing papers for them, and one day I read in The New York Times
about a play called Waiting for Godot
that was going on in Paris. It was a small clip, but it made me very interested. I got hold of it and read it in the French edition. It had something to say to me. Oddly enough, it had a sense of desolation, like Miller, though in its language, its lack of verbiage, it was the opposite of Miller. Still, the sense of a very contemporary lost soul was compelling. I got Wallace Fowlie to read it. His specialty was French literature. His judgment meant a lot to me even though he was so different from me. He was a convert to Catholicism, he was gay, and incredibly intelligent. He read the play and told me that he thought - and this before anybody had really heard about it much - that it would be one of the most important works of the 20th Century. And Sylvia Beach got involved in it somehow. She was a friend and admirer of Beckett. Waiting for Godot
just hit something in me. I got what Beckett writing was available and published it. He flew into the web and got trapped. He had been turned down by Simon and Schuster, I found out, much earlier, on an earlier novel.
In an interview with the Brooklyn Rail, Rosset spoke about the Henry Miller's Tropic of Capricorn being taken to court for obscenity charges:
We had a case in New York and, of course, he [Miller] wouldn’t go to the court. I had lunch with him at a restaurant on sixth Avenue right near here called Alfred’s with our lawyer and three or four other people, and then we had to go to court. But he wouldn’t go. He’d been summonsed so he was breaking the law by not going. So we went into court, and the District Attorney questioned me and said, “You see that we have a jury here of men and women with children who go to school right near where that book is on sale, near the subway stop. What’d you think they feel to have their children reading this book?” So I took out the book and started reading and the jury started laughing and they thought it was wonderful. I said to them, “If your children got this book and read the whole book you ought to congratulate them.” And they loved it, and they refused to convict me of anything. That was a great pleasure. Miller couldn’t leave this country until the decision was in, verified and so forth. For at least a year or two years, he couldn’t go. It was so funny because they accused me of soliciting him to write the book—write Tropic of Cancer and Capricorn—in Brooklyn, and at that point I was only 8 years old! Miller was a little older than me. It was a specific charge against me that was absurd. I was a pimp supposedly. They didn’t even bother to see how ridiculous their charge would look.
Launched in 1957, Evergreen Review pushed the limits of censorship, inspiring hundreds of thousands of younger Americans 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. In 2007, Rosset married Astrid Myers, then-managing editor of the online Evergreen Review. In 2008, Rosset completed writing his autobiography (now published as Rosset: My Life in Publishing and How I Fought Censorship. He died in 2012 after a double heart valve replacement.
Obscene, a documentary feature about Rosset by Neil Ortenberg and Daniel O’Connor, was released September 26, 2008. The film was a selection of the 2007 Toronto International Film Festival. Featured in the film are Amiri Baraka, Lenny Bruce, William S. Burroughs, Jim Carroll, Elsa Dorfman, Lawrence Ferlinghetti, Allen Ginsberg, Al Goldstein, Erica Jong, Ray Manzarek, Michael McClure, Henry Miller, John Rechy, Ed Sanders, Floyd Salas, John Sayles, Gore Vidal, John Waters and Malcolm X. A collection of film writing from Evergreen Review from the late 1950s to the early 1970s was published in 2017.
Rosset was awarded the French title Commandeur dans l'Ordre des Arts et des Lettres in 1999. He was honored by the National Coalition Against Censorship on October 21, 2008, for his work in defending free expression. On November 19, 2008, Rosset received the lifetime achievement Literarian Award from the National Book Foundation in honor of his contributions to American publishing. In 2012, he was awarded the Norman Mailer Prize for "Distinguished Publisher".