Averill was born in Bridgeport, Connecticut, where as a teenager she enjoyed drawing cartoons and writing. After graduating from Vassar College in 1923, she joined the editorial staff of Women's Wear Daily. In 1925 she moved to Paris, France as an assistant to a photojournalist. In 1931, Averill founded the Domino Press, which specialized in “children's picture books illustrated by gifted young artists and reproduced by means of the excellent color processes that were available”. Domino's first publication was Averill's book "Daniel Boone", illustrated by Feodor Rojankovsky, who later went on to win the Caldecott Medal for his children's illustrations. Domino Press published several more children's books before it ceased operations in 1938.

Averill returned to the United States in 1941. In 1944, she wrote and illustrated “The Cat Club”, the first in a series of stories about a cat, Jenny Linsky, who lived in New York City with her master, the benevolent Captain Tinker. Between 1944 and 1972, Averill wrote and illustrated a dozen more stories about Jenny Linsky and her cat friends, all of whom were based on cats Averill owned or knew.

Averill died in New York City on May 19, 1992.

The Cat Club, 1944

The School For Cats, 1947

Jenny's First Party, 1948

Jenny's Moonlight Adventure, 1949

When Jenny Lost Her Scarf, 1951

Jenny's Adopted Brothers, 1952

How the Brothers Joined the Cat Club, 1953

Jenny's Birthday Book, 1954

Jenny Goes to Sea, 1957

Jenny's Bedside Book, 1959

The Fire Cat, 1960

The Hotel Cat, 1969

Captains of the City Streets, 1972