Henry Markham was born in Wilmington, New York, and attended local schools before furthering his education at Wheeler's Academy in Vermont. He relocated to Wisconsin in 1861, where he enlisted in the Civil War, rising to the rank of second lieutenant. After being wounded in the Battle of Rivers' Bridge, he was discharged and subsequently studied law, passing the bar in 1867. Markham practiced law in Milwaukee before moving to Pasadena, California, in 1879, where he continued his legal career.