Born in London, Compton settled with his family in Bavaria in 1872 and painted throughout the Alps until 1914, becoming, alongside Gabriel Loppé, one of the two leading peintres-alpinistes of his generation. A skilled alpinist who climbed more than three hundred peaks in his lifetime - twenty-seven of them first ascents - Compton was one of the most prolific and topographically precise chroniclers of the Alps, working in oil, watercolour and pencil. He excelled particularly in watercolour, a medium in which his son and only pupil, Edward Harrison Compton, later noted his father seemed most at home.
Compton's range extended across the full breadth of the Alpine chain, from his frequently revisited Bernese Oberland and Monte Rosa massifs to more distant subjects such as the Ortler in the South Tyrol. He was a member of the Austro-German Alpine Club, the Swiss Alpine Club and the Alpine Club in London.