Joseph Moore was born in Washington County, Indiana, the son of John Parker Moore and Martha Cadwalader. In his early years, Moore attended Friends School and continued his education at the Blue River Academy. When he graduated at age 18, Moore began his teaching career. Three years later, Joseph left Blue River and entered Friends Boarding School. At age 27, Moore enrolled at Harvard to finish his education in science, earning a bachelor's degree.
In 1861, Moore left Harvard and returned to Earlham. In his science courses, he began to teach evolution, probably one of the first teachers in the Midwest to do so. He became president in 1868 and served until 1883. Moore not only served as president; he founded and expanded the Joseph Moore Museum, the natural history museum that remains an important part of Earlham's campus. Moore also was recorded a Friends minister in 1865 and was a leader in helping North Carolina Quakers recover after the Civil War.