An associate of Meyer Lansky, Greenbaum joined his organization on New York's Lower East Side in the mid or late 1910s. During Prohibition, Greenbaum began working with the Chicago Outfit managing the southwest division of the Trans-America Race wire service in 1928. Sent to Las Vegas shortly after World War II began, Greenbaum gained control over syndicate gambling operations with Morris Rosen and Moe Sedway. Sedway and Greenbaum ran the El Cortez Casino in 1945, until Greenbaum was asked by William R. Wilkerson to manage casino operations for the Flamingo Hotel. In 1946, Bugsy Siegel took over construction and creative control of the Flamingo, until it was shut down in January 1947 due to mounting losses as a result of Siegel's skimming.
After Siegel's murder in June 1947, Greenbaum brought the struggling casino out of debt within several months, controlling several other syndicate casinos and bookmaking operations in Arizona within several years. Greenbaum planned to retire to Arizona and rejected offers to run the Riviera for Tony Accardo, though after Greenbaum's sister-in-law was murdered, he accepted the job. As a syndicate leader in Las Vegas, Greenbaum would order the deaths of Tony Brancato and Tony Trombino for robbing a syndicate hotel. Shortly after his close friend and Chicago-enemy Willie Bioff's murder, Greenbaum's now worsening gambling, womanizing, and drug habits eventually caused him to begin skimming from casino operations. His embezzlement was discovered by the Chicago syndicate. On December 3, 1958, Greenbaum and his wife Bess were found dead in their Phoenix home. Their throats had been cut with a butcher knife. Gus was found in bed with a heating pad and his television turned on. He had nearly been decapitated. Bess sustained blunt trauma to her head before her throat was cut. Her head was padded with newspaper and a towel, seemingly to avoid blood stains on the furniture.
- "Hotelman, Wife Murdered". The Phoenix Arizona Republic (Phoenix). 4 December 1953. p. 1.
- Kelly, Robert J. Encyclopedia of Organized Crime in the United States. Westport, Connecticut: Greenwood Press, 2000. ISBN 0-313-30653-2
- Sifakis, Carl. The Mafia Encyclopedia. New York: Da Capo Press, 2005. ISBN 0-8160-5694-3
- Sifakis, Carl. The Encyclopedia of American Crime. New York: Facts on File Inc., 2001. ISBN 0-8160-4040-0
- Fried, Albert. The Rise and Fall of the Jewish Gangster in America. New York: Holt, Rinehart and Winston, 1980. ISBN 0-231-09683-6
- The Greenbaum Murder by John William Tuohy
- HiddenMysteries Conspiracy Archive - The Rest of the Story: THE ARIZONA PROJECT
- Phoenix New Times article by Dewey Webb