Born in Düsseldorf, von 1983 bis 1990 Finnendahl studied music composition and musicology with Frank Michael Beyer, Carl Dahlhaus and Gösta Neuwirth in Berlin.
He then studied from 1995 to 1998 with Helmut Lachenmann at the State University of Music and Performing Arts Stuttgart.
From 1988 to 1989 he studied at the California Institute of the Arts in Los Angeles.
In 2004 he became professor for composition at the Hochschule für Musik Freiburg.
Since 2013 Finnendahl has been professor of composition at the Hochschule für Musik und Darstellende Kunst Frankfurt am Main.