Born in Chicago, Illinois to a Jewish family, he began working in Vaudeville in 1922 as the straight man for his brother's jokes. He was also a cellist, a skill which he used throughout his career. By 1924, he was working in a speakeasy operated by Al Capone. After being caught in a gun fight, Amsterdam moved to California and sought work writing jokes. His enormous repertoire and ability to come up with a joke on any subject earned him the nickname "The Human Joke Machine."

During the 1930s, Amsterdam hosted a radio show and also wrote songs, including "Why Oh Why Did I Ever Leave Wyoming" and "Rum and Coca-Cola" (a popular hit that he copyrighted, although the song was based on a Trinidadian calypso). By 1947, he was performing on three daily radio shows.

Beginning in 1948, he appeared on the radio show Stop Me If You've Heard This One and began hosting his own television show, The Morey Amsterdam Show. The latter was replaced in 1950 by a variety and talk show called Broadway Open House, television's first late-night entertainment show, on the DuMont Television Network. Among his guests was a song and dance man named Art Carney.

Amsterdam's most famous role may have been as comedy writer Buddy Sorrell on The Dick Van Dyke Show (1961-1966), a role suggested for him by his friend Rose Marie, who also appeared on the show. Amsterdam wrote lyrics for the show's theme song that were never performed on the air but were performed by Dick Van Dyke in concert.

Amsterdam and Rose Marie later appeared as panelists on The Hollywood Squares and guest-starred together in a February 1996 episode of the NBC sitcom Caroline in the City, shortly before Amsterdam's death.

Amsterdam also was an occasional panelist on The Match Game during the early 1970s.

Amsterdam died of a heart attack in Los Angeles at the age of 87 and was interred in LA's Forest Lawn - Hollywood Hills Cemetery.