Möller was born in
Malmö, Sweden. He was educated in Stockholm at
Konstfack from 1870 to 1873, and at the
Royal Swedish Academy of Arts between 1873 and 1879, when he was awarded with the Royal Medal. The years 1879-1881, he made a study trip to
Germany,
France,
England,
Italy and
Austria and was in the winter of 1879-80 in Paris, as a student at the
École des Beaux-Arts (Atelier Guadet). He lived then in Stockholm, but made several trips abroad, especially to Paris. In 1881 he became architect in the Office of the Superintendent (
Överintendentsämbetet), a government agency in charge of public buildings, in 1903 Chief Curator, in 1904 Superintendent and 1918-1924 General Director of the
Board of Public Buildings (
Byggnadsstyrelsen), the successor agency of the Office of the Superintendent. In addition to his civil service career, Möller performed several assignments. He was the construction manager at the
General Art and Industrial Exposition of Stockholm (1897) and member of its central Committee, the same year member of the Administrative Committee for Sweden's participation in the
World's fair in Paris in 1900. In 1898 member of the Sanatorium Building Committee, member of the Royal Swedish Academy of Arts in 1890 and in 1901 a member of its management board, as well as honorary member of the
Royal Swedish Academy of Letters, History and Antiquities. Also in 1901 he was member of the Jubilee Fund's Board of Directors, in 1906 Chairman of the Technical School's Board of Directors and in 1911 President of the Committee of Regalia. He took part in the 1914
Baltic Exhibition in
Malmö, San Francisco Exhibition in 1915, and the 1925 Internal Art Industrial Exhibition in Paris. A bronze copy of the statue of Saint George and the Dragon was built on Möller's initiative and erected in 1912 in a street of Stockholm's
Old Town. Möller's most treasured works are in pure
Gothic style with splendid terrace construction like the neo-Gothic
St. John's Church, Stockholm (
S:t Johannes kyrka), which was inaugurated the 1890. In Stockholm, he led in 1891 the repair work on
Katarina Church (
Katarina Church) and in 1893 on
Saint James's Church (
Sankt Jacobs kyrka). All together he created or restored about 40 churches in Sweden as well as several schools buildings.{{cite web|url= https://www.svenskakyrkan.se/katarina/katarina-kyrka-och-allhelgonakyrkan|title= Katarina kyrka ==Buildings==