He first trained as a mason and later studied architecture at the Royal Danish Academy of Fine Arts in Copenhagen, graduating in 1920.

Their buildings also include the apartment blocks 2 Vodroffsvej (1930) and Vestersøhus (1935–1939) in Copenhagen, the latter of which has remained a major influence on Danish housing architecture.

[3] [4] Their winning proposal for Aarhus University consisted of individual faculty buildings arranged along the margin of an undulating park setting.

Møller was present at the construction site when the British Royal Air Force bombed the University dormitories, which were occupied by the Gestapo, on 31 October 1944.

During the attack, a bomb accidentally struck the main building, and Møller was lightly injured as a result, while about ten members of the construction crew were killed.