Steig was born in New York City to a family of aspiring artists. As a child, he dabbled in painting and was an avid reader of literature. Among other works, he was said to have been especially fascinated by Pinocchio. In addition to artistic endeavors, he also did well at athletics, being a member of the collegiate All-American water polo team. He never completed college, though he attended three of them, spending two years at City College of New York, three years at the National Academy of Design, and a mere five days at the Yale School of Fine Arts before dropping out of each.
When his family became caught in financial problems during the Great Depression, he began drawing cartoons as a freelance artist, and sold his first cartoon to the New Yorker in 1930. He soon became quite successful, and over the coming decades, he would publish over 1600 cartoons in the magazine, including 117 of its covers, leading Newsweek to dub him the "King of Cartoons."
In his 60s, he decided to try his hand at another artistic endeavor, and in 1968 wrote his first children's book. He excelled here as well, and his third book, Sylvester and the Magic Pebble (1970), won the prestigious Caldecott Medal. He went on to write more than thirty children's books, including famously the Doctor DeSoto series, continuing to write into his 90s. Among his other well-known works, the picture-book Shrek (1990) formed the basis for a widely successful 2001 movie of the same name.