After his studies of music in Munich Agop worked first for the Bayerische Landesbühne, a touring theatre, and then for three years as Kapellmeister and choir director at the Kärntner Grenzland-Theater in Klagenfurt. From 1945 to 1948 he was Kapellmeister at the Nürnberg Opera.
In 1949 Agop taught conducting at the Hochschule für Musik Detmold. From 1950 to 1952 he was the first principal conductor of the newly formed Nordwestdeutsche Philharmonie. He then was Generalmusikdirektor of the Dortmunder Philharmoniker. From 1962 to 1964 he conducted the Malmö Symphony Orchestra, and from 1962 to 1976 the Siegerlandorchester, later called Philharmonie Südwestfalen.
- "Gründungsgeschichte" (in German). Nordwestdeutsche Philharmonie. 2010. Retrieved 29 July 2010.