He was born on April 15, 1864 in Norwich, Connecticut, United States, the second child and first son among the ten children of George Case Setchell, at first a coffee and spice mill worker and later a manufacturer, and Mary Ann (Davis) Setchell.
His father's ancestors had emigrated from England in the late eighteenth century; his mother had come to the United States as a child with her English-Welsh parents. Setchell early showed a strong interest in natural history, especially botany. The gift of a copy of Familiar Lectures on Botany, by Almira Hart Lincoln Phelps, helped him determine the names of many of the local plants. This experience at identification foreshadowed his later work in systematics, a branch of botany in which he made great contributions.