Henry was born in Charleston but, orphaned early, was brought up by relatives in New York. He studied art first with the New York painter Walter M. Oddie and, in 1858, at the Pennsylvania Academy of Fine Arts in Philadelphia. In 1860, Henry traveled to Paris, where he studied with Charles Gleyre and Gustave Courbet. He returned to New York in 1860 and took a studio in the 10th Street Studio Building.
Henry was popular during his lifetime because of his high academic standards as a painter. His works were highly finished and filled with fine details. He used photographs, local models, and animals; he often painted horses outdoors, but when he could not, he had a papier-mâché horse made for his studio. He kept a collection of historical costumes and props for his models. Henry’s work was frequently reproduced during his lifetime as lithographs, and appeared in popular magazines. Like the work of J.C. Leyendecker, Henry’s paintings lent themselves to illustration.