He had financed his studies with a jazz ensemble, working for the British military broadcasters (britischen Besatzungsmacht betriebene Sendergruppe Alpenland) and the Styrian Provincial Theatre.
On 15 July 1996, he married Gabriela Elias, an Austrian author, museum curator and cultural journalist.
In 1953, Koschatzky joined the Office of the Styrian Government, and moved in 1955 to the Neue Galerie at the Universalmuseum Joanneum in Graz where he worked from 1956 to 1961 as a director.
From 1 January 1962 to 1 October 1986 he was appointed, by Minister of Education Henry Drimmel, as director of the collection of Prints and Drawings at the Albertina in Vienna.
In 1972, there were exhibitions of important drawings from the Albertina in Moscow and Leningrad; in 1985 in Washington DC and in New York City.