Together with his fellow painter and friend Christoffer Wilhelm Eckersberg Møller moved to Copenhagen in 1803 to study at the Royal Danish Academy of Fine Arts.
At the Academy he won the silver medal and was the first student of Nicolai Abildgaard and later was taught by Christian August Lorentzen.
At the same time Møller decided to learn how to restore paintings In 1810 he received a travel grant partly by the Prince's support.
As early as 1814 Møller had been appointed curator at the royal collection of paintings and was for some years a drawing teacher for midshipmen.
Møller received the medal "Ingenio an arte" in 1842 for a difficult restoration of Queen Caroline Amalie's portrait.