Koenig studied church music in Braunschweig, composition, piano, analysis, and acoustics in Detmold, music representation techniques in Cologne, and computer technique in Bonn. He attended the Darmstadt music summer schools for several years, and later returned as a lecturer. From 1954 to 1964, Koenig worked in the electronic music studio of West German Radio at Cologne, assisting other composers (including Stockhausen, Kagel, Evangelisti, Ligeti, and Brün), and producing his own electronic compositions. During this period he also wrote orchestral and chamber music for piano, string quartet, and woodwind quintet.

From 1958 he was an assistant in the radio drama department at the Cologne academy of music, and taught electronic music, composition, and analysis from 1962. In 1964 Koenig moved to the Netherlands. Until 1986 he served as director and later chairman of the Institute of Sonology at the University of Utrecht. During this period the Institute acquired a worldwide reputation, particularly for its annual Sonology course. Koenig also lectured extensively in the Netherlands and other countries and developed his computer programs "Project 1", "Project 2", and "SSP", designed to formalise the composition of musical structure-variants. These were followed by the application of his computer programs, resulting in chamber music (Übung for piano, the Segmente series, 3 ASKO Pieces, String Quartet 1987, String Trio) and works for orchestra (Beitrag, Concerti e Corali).

Since 1986, when the Institute moved from Utrecht University to the Royal Conservatory at The Hague, Koenig has continued to compose, produce computer graphics, and develop musical expert systems. The first three volumes of his theoretical writings were published between 1991 and 1993 under the title Ästhetische Praxis by Pfau Verlag; an Italian selection appeared under the title "Genesi e forma" (Semar, Rome 1995). A fourth volume followed in 1999, a fifth in 2002; the sixth (2007) contains a complete thematic index. In 1961 Koenig received an incentive award from the Federal State of North Rhine-Westphalia, in 1987 the Matthijs Vermeulen Prize from the City of Amsterdam, and in 1991 the Christoph and Stephan Kaske Prize. In 2002, the Philosophical Faculty of the University of Saarbrücken, Germany awarded Koenig an honourary doctorate. In the winter semester of 2002/2003 he was Visiting Professor for Computer Music at the Technical University, Berlin. In 2010 Koenig received the Giga-Hertz Prize of ZKM, Karlsruhe.