Orbach was born in the Bronx on October 20, 1935 to Leon Orbach, a former vaudevillian, and Emily Orbach, a radio singer. After spending a childhood in Westchester, Pennsylvania, Massachusetts and Illinois, he studied drama at the University of Illinois and Northwestern Unversity in the early 1950s. He made his stage debut in a summer stock production of the farce Room Service as a teenager and his professional New York debut at the age of 21, in a revival of The Threepenny Opera, eventually assuming the lead role of Macheath.
In 1960, Orbach played his first of many legendary stage roles as El Gallo in the original off-Broadway company of The Fantasticks, introducing the iconic song "Try to Remember" to the world. A breakthrough on Broadway came several years later with a Tony-nominated turn as Sky Masterson in the 1965 revival of Guys and Dolls. Orbach won a Tony four years later for the hit musical Promises, Promises as well as a Drama Desk Award and received a third and final nomination in 1976 for originating the role of Billy Flynn in Chicago. His other Broadway credits include The Threepenny Opera, Carnival!, Annie Get Your Gun, The Natural Look, 8 Rms Riv Vu and the original production of 42nd Street as impresario Julian Marsh.
Orbach's big screen credits include The Gang That Couldn't Shoot Straight, Fore Play, The Sentinel, Prince of the City, Brewster's Millions, F/X, Dirty Dancing, Someone to Watch Over Me, Last Exit to Brooklyn, Crimes and Misdemeanors, Out for Justice, Straight Talk, Mr. Saturday Night, The Cemetery Club, Chinese Coffee, Prince of Central Park and creating the voice of Lumiere in the original Oscar-nominated Beauty and the Beast and its subsequent video sequels.
Orbach was diagnosed with prostate cancer in early December 2004. He is survived by wife Elaine Orbach and sons Anthony Orbach and Christopher Orbach.