He studied musicology, philosophy and medieval Latin at the University of Heidelberg, where he worked with Thrasybulos Georgiades and received the PhD in 1957.
He was appointed chairman of the music commission of the Bayerische Akademie der Wissenschaften in 1982 and member of the European Academy of Sciences and Arts in 1991.
The chair, or Lehrstuhl, of musicology at the university's Institut fuer Musikwissenschaft has been held by Adolf Sandberger, Rudolf von Ficker, Thrasybulos Georgiades and (from 1973 ) Professor Göllner.
von Ficker, Georgiades and Göllner were also chairmen of the Musikhistorische Kommission of the Bayerische Akademie der Wissenschaften, which, among other projects, is responsible for the complete Orlando di Lasso edition.
The Gesellschaft für Bayerische Musikgeschichte, founded in 1958, is devoted to research and publication of musicological manuscripts [2] Göllner was married to Marie Louise Göllner (nee Martinez), a retired professor of music history and former chair of the music department at the University of California, Los Angeles, where she worked from 1973 to 2000.