He was born at Bøn, Eidsvoll to factory owner Hartwig Bache-Wiig (1850–1922) and his wife Amalie Kristine Holt (1851–1940).
He first attended the West Saxon University of Applied Sciences of Zwickau, and then the Karlsruhe Institute of Technology, where he took his final exam in 1902.
After that, he was appointed professor in electrical engineering at the newly established Norwegian Institute of Technology, where he stayed until 1916.
Four years later, he resigned from the position, in protest against the New York head office intervening in his area of responsibility.
[1] During the Quisling regime of German-occupied Norway, Bache-Wiig served in the non-political Administrative Council until September 1940, when it was replaced by the Reichskommissariat Norwegen headed by the Norwegian Nazi Terboven.