He studied at the Royal Danish Academy of Fine Arts and began his career working for Danish architect Kaare Klint. Together, they developed the concept of functionalist design, which emphasized the simplicity, durability and functionality of objects.
Koch has designed many iconic pieces of furniture, including the "Safari Chair", the "MK99200 Table" and the "Bookcase System", all of which have been acclaimed for their elegance and functionality.
In addition to his furniture design work, Koch has also worked on architectural projects, such as the design of the Grøndalskirken church in Copenhagen.
Over the course of his career, Koch has received numerous awards and honors for his work, including the prestigious C.F. Hansen Award in 1972. Today, his work is exhibited in museums around the world, including the Museum of Modern Art in New York and the Designmuseum Danmark.