Born in Sand Bank, New York in 1885, Avery and his family moved to Hartford, Connecticut in 1898. He enrolled in a lettering class at the Connecticut League of Art Students in Hartford in 1905 and soon after was persuaded by the school's director, Charles Noel Flagg, to transfer to a life-drawing class. This decision would launch his career in fine arts.
In 1918, while holding down jobs as a clerk and construction worker, Avery attended the School of Art at the Society of Hartford and in 1924 he became a member of the Connecticut Academy of Fine Arts. He befriended Adolph Gottlieb, Mark Rothko and Barnett Newman while attending sketch classes at the Arts Students League in New York.
Avery began to experiment with monotypes in 1949 and by 1952 he began working in woodcut. His works have been exhibited at the Phillips Memorial Gallery, the Art Institute of Chicago, and the Durand- Ruel Galleries in New York.