He was born in Trondhjem as the son of Ludvig Wiese Knagenhjelm (1824–1907) and Selma Angelique Lousie Roll.
[1] The Knagenhjelm family had resided in Sogndal in recent times, and had been ennobled in 1721, then under the name Knagenhielm.
Arthur and Barbara had the son Kai Knagenhjelm, a high-ranking bureaucrat who married into the Sverdrup Fearnley family.
He was a deputy judge from 1889 to 1891, then a junior solicitor from 1892 to 1895, working in the Office of the Attorney General of Norway.
He was a board member of Glommens Brukseierforening from 1903, Salomons Skofabrik from 1904, Labro Træsliberi from 1906 to 1918, Hafslund from 1916 to 1922, Freia Chocolade Fabrik from 1916, Odda Smelteverk from 1924; and a supervisory council member of Filharmonisk Selskap.