Matthus attended secondary school in Rheinsberg, followed with studies the Hochschule fuer Musik in Berlin. After graduating, he continued his studies in composition with Rudolf Wagner-Regeny and Hanns Eisler, and was shortly thereafter made the youngest composer in residence in the history of the Komische Oper Berlin by Walter Felsenstein. Matthus has written more than a dozen stage works sense, including Graf Mirabeau (1987-88), an opera set during the French Revolution which was commissioned for the 200th anniversary of Bastille Day and enjoyed simultaneous productions in both East and West Germany as well as Czechoslovakia, the Soviet Union and France. The opera has also been recorded by the Berlin State Opera. Other opera recordings include his Old Testament-based "opera vision" Judith (1984) by the Komische Oper Berlin and his Der letzte Schuss with the Berlin Radio Symphony Orchestra. Recently, he composed music for both a ballet and an opera adaptation of Michael Ende's The Neverending Story (2003).
Matthus has also been a prolific composer of works for orchestra as well as chamber and recital compositions. He has enjoyed a close working relationship with conductor Kurt Masur who has presented many world premieres of his music, including what Matthus has called "the commission of my life," a Te Deum for the reconsecration of the Dresden Frauenkirche. His works are featured on more than twenty recordings by several of Germany's leading symphony orchestras and chamber music ensembles.
Matthus is currently the Artistic Director of the Kammeroper Rheinsberg where he has served since 1991. He is also the founder and director of the Rheinsberg Music Festival and an honorary citizen of the city of Rheinsberg.
On January 25, 2009, Leon Botstein and the American Symphony Orchestra presented the New York premiere performance of Matthus's "Responso," a four-movement symphony written in 1977.