Powell was born in Mount Morris, New York, in 1834, the son of Joseph and Mary Powell. His father, a poor itinerant preacher, had emigrated to the U.S. from Shrewsbury, England, in 1830. His family moved westward to Jackson, Ohio, then Walworth County, Wisconsin, before settling in Illinois in rural Boone County.

Powell studied at Illinois College, Wheaton College and Oberlin College, acquiring a knowledge of Ancient Greek and Latin. Powell had a restless nature and a deep interest in the natural sciences. As a young man he undertook a series of adventures through the Mississippi River valley. In 1855, he spent four months walking across Wisconsin. During 1856, he rowed the Mississippi from St. Anthony, Minnesota, to the sea. In 1857, he rowed down the Ohio River from Pittsburgh to St. Louis; and in 1858 down the Illinois River, then up the Mississippi and the Des Moines River to central Iowa. At age 25 he was elected to the Illinois Natural History Society in 1859.