Moeller was born on 1 August 1806 in Münster, Germany, the son of Elisabeth Charlotte Alberti, from Hamburg,[1] and Jacob Nicolai Møller, a Norwegian whose conversion to Catholicism had excluded him from public office in Denmark–Norway.
[3] He studied at the Gymnasium in Nuremberg where Georg Wilhelm Friedrich Hegel was headmaster, then in Prague and finally in Dresden, where his uncle Ludwig Tieck, his mother's sister's husband,[3] was then living.
He wrote several textbooks on medieval and universal history, as well as numerous articles in scholarly journals and the general press.
[5] One of his sons, Jean Moeller, died of his wounds after the Battle of Mentana in 1867, while serving with the Papal Zouaves.
[6] His grandson, Alfred Alphonse Moeller, became a colonial administrator, governor of Orientale Province in the Belgian Congo, and later a businessman.