Waldman was born in Brooklyn, New York. He was a graduate of the Pratt Institute, where he majored in Art. He started his first career work in 1930 at Fleischer Studio. At Fleischer he worked on Betty Boop, Raggedy Ann, Gulliver's Travels, the animated adaptations of Superman, and Popeye. He was head animator on two Academy Award nominated shorts, Educated Fish (1937) and Hunky and Spunky (1939).
Waldman made the transition when Fleischer Studios was foreclosed on by Paramount Pictures and reorganized as Famous Studios in 1942. At Famous he worked mostly on the Casper the Friendly Ghost series. In 1958 he left Famous to become an animation director at Hal Seeger Productions where he worked on the revival of the Out of the Inkwell series, as well as Milton the Monster, until his retirement in 1968.
Outside of animation, Waldman partnered with writer Steve Carlin in 1940 to produce the Happy the Humbug comic strip. He also created one of the first graphic novels, Eve: A Pictorial Love Story(1943).
In 1986 Waldman received the Motion Picture Screen Cartoonists Award, and in 1997 was given the Winsor McCay Award for his lifetime work in the field of animation. Waldman died of congestive heart failure at the age of 97 in Bethpage, New York.