Almost the entire territory of Austria belongs to the Black Sea basin and is drained by the Danube, the country's main river.

An excerpt from the article 31 facts about Austria

Austria's largest rivers have their sources outside the country. The Danube has its source near Donaueschingen, in southwestern Germany. Before it flows into the Black Sea, it flows through Austria. It is the only large European river that flows from west to east. The importance of the Danube as a communication route has always been very great, and it even increased after the construction of the Rhine-Main-Danube canal in 1992. This canal connects the Black Sea with the North Sea.