Arch E. Cole was born in Ohio, the son of Henry and Isabella Grey Cole. He graduated from Ohio Wesleyan University in 1916, and the University of Wisconsin with a PhD in Anatomy in 1920. Dr. Cole came to the University of Louisville in 1929 and at the time of his death was acting Chair of Anatomy. Students voted him pre-clinical professor of the year five times during his career at UofL. He married Blanche Stotts, and they had three children, Dr. Arch E. Cole, Jr., Patricia Collier and Mildred Kempf.
The Arch E. Cole Scholarship for Academic Excellence at the University of Louisville School of Medicine is given in his honor each year to a third and fourth year student.