Melling was born Anton Ignaz Melling in Karlsruhe, Baden, in 1763. After the death of his sculptor father, he lived with his painter uncle, Joseph Melling, in Strassbourg (Alsace). As a young man he visited his older brother, and studied Architecture and Mathematics at Klagenfurt. At the age of 19, he went to Italy, Egypt, and finally Constantinople as a member of the Russian Ambassador's retinue and household with the aim of drawing pictures for various dignitaries. He was introduced to princess Hatice Sultan, sister and confidant of the Ottoman Sultan Selim III.