 He was born in the Calmeyerløkken neighborhood of Kristiania (now Oslo) and grew up in Kristiania with his brothers, including the marine biologist Jonas Axel Boeck (1833–1873).In 1866 Boeck married Julie Pauline Louise Maschmann (1841–1923), the daughter of the priest Bernt Sverdrup Maschmann (1805–1869).In 1889, Boeck's daughter Elisabeth (1868–1958) married the architect Herman Backer (1856–1932).