[2] Born in Copenhagen, Møller studied at the Royal Danish Academy of Fine Arts under Gottfred Eickhoff and Richard Mortensen (1962–66).
In the 1960s, together with Hein Heinsen and Stig Brøgger, he was one of those who brought American trends in Minimalism to Denmark.
[3] Møller then moved into sculpture where he could better represent mass media's oversimplification of a complex world.
The portrait of Queen Margrethe on Danish 10 and 20 kroner coins since 2001 is the work of Mogens Møller.
From 2004 to 2007, together with Heinsen and Brøgger, he carried out comprehensive decoration work at the Ollerup School of Gymnastics on the island of Funen.