Koch was raised in Ann Arbor, Michigan. At the age of fourteen, without the encouragement or technical guidance of any teacher of art, he began to paint. Summers of 1927 and 1928 spent on Cape Cod, Massachusetts, provided an opportunity to observe Charles Hawthorne's classes at work. Later in 1928 Koch went to Paris to continue his independent study of art. There he gave great attention to the Old Master paintings in the Louvre, being particularly influenced by the great colorists of the Baroque, such as Rubens and Tintoretto. On his return to America in 1933, he settled permanently in New York. His first one-man exhibition was presented by the Kraushaar Galleries, New York, in 1939; Kraushaar would remained his principle representative throughout his life.
Koch's favored subject was social gatherings in well- appointed Manhattan apartment interiors, where the grace and ease of the occasion was complemented by the objets d'art and paintings that characterized the settings. For a number of years, Koch and his wife, the concert pianist Dora Zaslavsy, held a Sunday afternoon "salon" in their Manhattan home, which was attended by a number of their friends from the world of art, music and literature, among whom were Leo Lerman, Virgil Thompson, Roger Bacon, and Maurice Grosser. Several of his paintings depicted these occasions, with all the figures being portraits. Koch's work was essentially freely-brushed, academic realism in style. In his particular attention to the rendering of the light of interior spaces, he reflected more an admiration and study of the Dutch and Flemish masters, such as Vermeer, than of Impressionism. Koch also worked extensively as a portraitist, and was known for his images of the wealthy and celebrated, among whom were H. R. H. Princess Margaret of Great Britain, and the composer, Richard Rogers.
Koch was an active member of the Academy's Council, serving three terms as assistant treasurer from 1957 to 1960, as assistant corresponding secretary for the year 1962-63, and first vice president from 1963 to 1965. He taught at the New York Art Students League from 1944 to 1946, and although never a member of the Academy school's faculty, he chaired its school committee for a part of the period of his Council service.
For paintings shown in Academy annual exhibitons, he received Altman prizes in 1959 and 1964; the Saltus Medal, 1962; the Morse Medal, 1968; and the Engel Prize, 1972. His work was also honored by the Audubon Artists; the Lotos Club, New York; and the Butler Institute of American Art, Youngstown, Ohio. Koch was a member of the National Institute of Arts and Letters, the Royal Society of Artists, and the International Academy of Literature, Arts and Sciences.