He was born in Kolozsvár/Klausenburg, Transylvania, Kingdom of Hungary, Austro-Hungarian Empire, nowadays called Cluj-Napoca, Romania, and died in Bern.
Veress studied and later taught at the Franz Liszt Academy in Budapest.
Among his teachers were Zoltán Kodály, with whom he studied composition, and Béla Bartók, with whom he studied piano; as an assistant to László Lajtha he did field research on Hungarian, Transylvanian, and Moldavian folk music.
Among the composers who studied under him are György Ligeti, György Kurtág, Heinz Holliger, Heinz Marti, Jürg Wyttenbach and Roland Moser.
He wrote numerous chamber music pieces and symphonic works.