He studied sculpture at the Berlin Academy of Fine Arts before working as a graphic and furniture designer. In the early 1930s, he joined the industrial design firm Berliner Metallgewerbe Joseph Müller and began working on product design projects such as household appliances and office equipment.
After the Second World War, Moller founded his own industrial design office in Stuttgart and began working with companies such as Braun, Telefunken and Daimler-Benz. He is best known for his television designs for Braun, notably the SK4 model, also known as "Snow White's Coffin" due to its cubic shape and white Plexiglas covering.
Moller was also involved in the development of the new city of Wolfsburg in Germany, where he worked on urban planning and building design projects.
His work has influenced many designers and continues to be recognized as a benchmark in the field of industrial design.