He is a graduate of the School of Industrial Art in New York City. While still in high school, he was an apprentice in the studio of Lucian Bernhard, the great German graphic designer. He also found a mentor in Ervine Metzl, illustrator and President of the Society of Illustrators, who predicted that the young Mr. Barrett "...would either wind up in a mental institution or make a million dollars."

After early success as an art director at Young & Rubicam and Carl Ally, winning the Gold Medal of the Art Directors Club of New York, he left advertising to become an illustrator, author and puzzle maker. He wrote The Nutty News and has illustrated many books, such as a series of children's books with Judi Barrett, including Cloudy with a Chance of Meatballs and Animals Should Definitely Not Wear Clothing. He has also worked on several books for adults, including the best-selling O. J.'s Legal Pad with Henry Beard and John Boswell. In 2009 Cloudy With a Chance of Meatballs became an animated feature in 3D, created by Sony Animation.

During the 1970s, Barrett had many comic strips in the National Lampoon "Funny Pages", of which the best remembered is perhaps "Politeness Man".