Compton was born in Stoke Newington in London, the son of Theodore Compton, an art-loving insurance agent, and grew up in a deeply religious Quaker household. He attended various art schools, including, for a time, the Royal Academy in London, but otherwise he was mainly self-taught in art.
In 1867, wanting the best education for their artistically-talented son, and due to the high cost of schooling in England, the family decided to emigrate to Germany settling in Darmstadt. The city at that time was the seat of the Grand Duchy of Hesse under Grand Duke Ludwig III, and a community of artists had sprung up there. Entries in Comptons diary show that both he and his father were art teachers - Alice, the Princess of Hesse numbered amongst Edwards students.