Mayer was born in Little Rock, Arkansas. His father was in the United States Navy, so the family moved many times during his childhood before settling in Honolulu, Hawaii. There, Mayer graduated from high school in 1961. While attending school at the Honolulu Museum of Art, Mayer decided to enter the field of children's book illustration. To that end, he created a portfolio of sketches and peddled them wherever he could. Though his professors feared the young artist would never be good enough to make a living as an illustrator, Mayer was not dissuaded.

Mayer moved from Hawaii to New York City in 1964, pursuing further instruction at the Art Students League of New York, where he met an artist named Marianna who became his first wife. He also met an art director who told Mayer that his portfolio was so bad that he needed to throw it away. Though offended, Mayer did. During his spare time from his job at an advertising agency, the artist created a completely new portfolio. These new sketches persuaded editors at Dial Press and Harper & Row to give him some illustration work.

Mayer published his first book, A Boy, a Dog, and a Frog, at Dial Press in 1967. It was notable for being a completely wordless picture bookone that tells its story entirely through the use of pictures. Mayer was one of the first illustrators to be credited for using this format. Five more books in this series were to follow.

The book There's a Nightmare in My Closet drew on Mayer's childhood fears of monsters in his room at night. Critics compared the book, unfavorably, to Maurice Sendak's Where the Wild Things Are, but children and their parents loved the story and it became very popular.

Mayer joined Golden Publishing, creators of Little Golden Books, in 1976. Through them he has sold his "Little Critter" and "Little Monster" series, which are popular with beginning readers.

In 1978, Mayer divorced Marianna. The following year, he married his second wife, Jo. The couple had three children, Len, Arden and a daughter named Jessie. Mayer and his third wife Gina, with whom he had two more sons (Ben and Zebulon) currently live in Roxbury, Connecticut. Gina has been collaborating with him on many of his books since the early 1990s.