Born in Stuttgart, Küster studied musicology, Medieval and Modern History and Comparative Regional Studies at the Eberhard Karls University Tübingen and received his doctorate in 1989 with a thesis on the design of the first movements in Mozart's concerts (Kassel 1991).
In 1993 he habilitated in Freiburg with the thesis Opus primum in Venice - tradition of the vocal movement, 1590-1650.
[1] Küster's spectrum of research covers a wide range from the music of the Middle Ages to the Protestant musical culture of the 16th to 19th centuries (especially Heinrich Schütz and Johann Sebastian Bach) and on to First Viennese School.
He became known as the editor of the Bach Handbook[2] A main focus of his work is music in northern Central Europe, especially organ culture in the marshes on the North Sea.
In connection with the Evangelical Lutheran Church in Northern Germany, he conceived the touring exhibition "Organs at the North Sea - Culture of the Marshes"[3] in 2013.