Cleveland was born in Ohio in 1837 to a successful lawyer and businessman and his wife. He attended preparatory school in Troy, New York, and ultimately attended what is now New York University for mechanical engineering. With his early training in art and engineering, he soon landed a position with the United State Coast Survey, one of the oldest Federal government departments.

His career as surveyor and mapmaker took him up and down the East Coast until the outbreak of the American Civil War. He served as a Captain in the Union Army for the duration of the war, and his mapmaking was instrumental in aiding the Northern effort. After the war he was sent to survey parts of Colombia, in South America. At this point his life moved westward, and he spent some years living in the San Francisco area before moving to Portland, Oregon. While there he charted large areas of the Pacific Northwest, travelling to Alaska and British Columbia, where he completed many sketches that would become the basis of his painting work in retirement. Unsurprisingly, his expertise in cartography and mapmaking made him a meticulous painter of landscapes he had seen. He is best know for his finely detailed watercolors and oils of Pacific Northwest land- and seascapes.