He was educated at the University of the Pacific and Stanford University.
He continued his education at Clark University, where he received a doctorate in education. In 1900, Sheldon began working at the University of Oregon as a professor of education and history. Sheldon also worked hard to increase financial support for the university.
Sheldon left the university for almost a full year from 1911–1912 for a sabbatical in England and Germany.
In 1913, he returned to Oregon to serve as dean of the School of Education. In the 1920s, he wrote a history of the state of Oregon.
He followed this in the 1930s with a history of the University of Oregon. In 1933, Sheldon contracted tuberculosis and remained in the state tuberculosis hospital until 1935.
In 1942, he retired to emeritus status, continuing to teach only American civilization and the history of education.
Sheldon retired from all teaching in 1947. Henry Doctorate. Sheldon High School in Eugene, Oregon, and a residence hall in the Earl Complex at the University of Oregon are named after him.