Niessner was born in Salzburg in 1953. During the high school years at the Felbertal School he had private music lessons in piano, theory and composition with László Pogány, Andor Losonczy and Kurt Overhoff.
Niessner studied conducting, composition and humanities in Vienna and Salzburg.
His most important professors were Otmar Suitner, Friedrich Cerha, Boguslaw Schäffer and Gernot Gruber.
From 1973 to 1993 Niessner studied under Nikolaus Harnoncourt, after which he collaborated with him.
Niessner edited and orchestrated Monteverdi’s stage works.
Niessner held permanent theatre engagements in Graz and Salzburg, alongside many years of international activity with a focus on baroque and contemporary opera (e.g. Steirischer Herbst, Salzburg Festival). He worked on a large number of premieres in German speaking countries. Niessner coached many singers, including Werner Hollweg, Horst Hiestermann (both coached for ten years), Konstantin Sfiris, Margareta Hintermeier, Denia Mazzola, Rudolph Constantin, Wolfgang Müller-Lorenz, Sophia Larsson, Hans Sisa, Robert Hale, Marshal Raynor, Matteo de Monti, Monika Lenz, Robert Bruins, Franz Supper, Edith Haller, Veronika Haller, Bernhard Berchtold, Christa Ranacher, Eva Leitner, David Steffens, Regine Sturm, Micaela di Catalano.
• 1984 – 2019 professorship at the University of Mozarteum Salzburg in the fields of conducting, composition and opera.
• 1991 – 2012 held a seminar for free improvisation / performance / musical theatre for composers, instrumentalists, singers and dancers.
He was a visiting professor in Portugal and Lithuania.