Born in New York City as Albert Eliot Moshinsky, he made his Broadway debut as an actor and associate director of the 1950 revival of John Vanbrugh's Restoration comedy The Relapse. Three years later he helmed a production of Shaw's Misalliance, followed by Kismet, for which he received the 1954 Donaldson Award (precursor to the Tonys) for Best Director of a Musical. The cast of Kismet included Alfred Drake, Doretta Morrow, Richard Kiley and Joan Diener. Diener would become Marre's wife in 1956, the same year he was nominated for the Tony Award for Best Director for The Chalk Garden. That same year he also directed a revival of Shaw's Saint Joan starring Irish actress Siobhán McKenna.
In 1958, Marre directed the Jean Anouilh play, Time Remembered (translated by Patricia Moyes), which starred Helen Hayes, Richard Burton, Susan Strasberg and Sig Arno. The production won five Tony nominations including Best Play, and Hayes took home the prize for Best Actress. The same year, he directed a production of At the Grand, a musical version of Vicki Baum's 1930 novel, Grand Hotel, in Los Angeles, with Marre's wife, Joan Diener, as the opera diva who falls in love with a charming, but larcenous, faux baron.
Marre returned to New York where he scored with Jerry Herman's first Broadway musical, Milk and Honey, nominated for five Tony Awards including Best Musical. He also directed a revival of Shaw's little-known Too True to Be Good, with an all-star cast. A couple of misfires were followed by what proved to be his greatest success, Dale Wasserman, Joe Darion and Mitch Leigh's Man of La Mancha, again pairing Kiley and Diener. Marre won the Tony Award for Best Director of a Musical and went on to direct numerous national and international productions of the hit, as well as the Broadway revivals in 1972, 1977, and 1992. (He was signed to direct the screen version but was replaced first by Peter Glenville, and ultimately by Arthur Hiller, after artistic differences with United Artists executives. The finished film, starring Peter O'Toole and Sophia Loren, was critically and financially unsuccessful.)
Marre's subsequent collaborations with Leigh and his wife, the musicals Cry for Us All (1970) and Home Sweet Homer (1976), were not successful. Marre directed two versions of Chu Chem, a musical by Leigh, Ted Allan, Jim Haines and Jack Wohl. The original in 1966, starring Menasha Skulnick and Molly Picon, closed out of town in Philadelphia), while a second version opened off-Broadway in 1988 at the Jewish Repertory Theatre in New York. Buoyed by good reviews from critics at The New York Times and The New York Post, the show was subsequently moved to Broadway in 1989, where it was not as well received.
In 1948, Marre was one of the co-founders of the historic Brattle Theatre in Cambridge, Massachusetts, one of the country's first classical repertory companies (and one not build on the not-for-profit model), which yielded five years of classics and new plays, many of which moved on to subsequent New York productions. In 1953, he was hired by Lincoln Kirstein to be the first Artistic Director for Theater at City Center, where he oversaw its first theatrical season. He was an active director in both London and Los Angeles, particularly for Los Angeles Civic Light Opera Company, where he directed many major star-studded revivals including Burt Lancaster in Knickerbocker Holiday. He directed the inaugural production at the Ahmanson Theatre/Los Angeles Music Center, The Sorrows of Frederick by Romulus Linney, which starred Fritz Weaver.
In the late 1940s, Marre was married to actress Jan Farrand, who played numerous leads with the Brattle Theatre and later on Broadway, but the marriage ended in divorce. Marre and actress Joan Diener wed in 1956, had two children, Jennifer and Adam, and remained married until her death in 2006.
In 2009, Marre married actress-lyricist Mimi Turque, to whom he remained wed until his death three years later, on September 4, 2012, aged 87, at Mt. Sinai Hospital, New York City, after a long illness. Turque had played Antonia, Don Quixote's niece, in the original production of Man of La Mancha.