Piston was born in Rockland, Maine at 15 Ocean Street to Walter Hamor Piston, a bookkeeper, and Leona Stover. He was the second of four children. Although his family was mainly of English origin, his paternal grandfather was a sailor named Antonio Pistone, who changed his name to Anthony Piston when he came to Maine from Genoa, Italy. In 1905 the composer's father, Walter Piston Sr, moved with his family to Boston, Massachusetts.