Leeds was born on April 6, 1916 in New York City, the son of a post office clerk. Raised in the Bronx, he was a Peanut vendor for some time near Yankee Stadium and Manhattan's Polo Grounds. He started his career as a standup Comedian and then went on to appear in several films and sitcoms, including Rosemary's Baby, Beaches, All in the Family, Three's Company, Night Court, Wings, Ally McBeal, Everybody Loves Raymond, The Larry Sanders Show, Barney Miller, Car 54, Where Are You?, The Patty Duke Show, The Monkees, The Odd Couple, Happy Days, Friends, Mad About You, The Dick Van Dyke Show and The Golden Girls.