Joch was born on 4 September 1787 in Christianshavn, Copenhagen, the son of Jørgen Hansen Koch (1746–1801), a ship builder, and Anne Cathrine née Folkersen (1758–1809).

In 1818, together with the sculptor Hermann Ernst Freund,[1] he traveled to Rome where he met Bertel Thorvaldsen and other members of the Danish artists' colony who resided in the city at that time.

Back in Denmark, Koch was appointed Royal Master Builder, succeeding Christian Frederik Hansen as the leader of the national building administration.

[3] Koch was responsible for a number of renovations and reconstructions of Royal residences, including Brockdorff's Palace (1827–1828) and Bernstorff's Mansion [da] (1829).

Andersen also developed a friendly relationship with their children which continued after the parents' death, as did the dinner arrangement on Fridays.