Giselher Klebe was born in Mannheim, Germany. He received musical tuition early in his life from his mother, the violinist Gertrud Klebe. The family relocated in 1932 to Munich, where his mother's sister, Melanie Michaelis, continued the training. His father's profession required a further relocation in 1936 to Rostock.
Following the separation of his parents, Klebe moved with his mother and sister to Berlin. During 1938, the 13-year-old sketched his first compositions. In 1940, he began studies in violin, viola, and composition, supported by a grant from the city of Berlin.
After serving his Reichsarbeitsdienst (labour service), Klebe was conscripted to military service as signalman. After the German surrender, he was taken prisoner of war by the Russian forces. Due to ill health, he was soon released.
Having convalesced, Klebe continued his music studies in Berlin (1946–1951), first under Joseph Rufer, then in master classes by Boris Blacher. He worked for the radio station Berliner Rundfunk until 1948, when he began to work full-time as a composer.
Klebe was inspired and influenced by works of authors and artists, especially his contemporaries. In 1951 he composed Die Zwitschermaschine Op. 7, (The Twittering Machine), based on the by Paul Klee. His first opera, based on Friedrich Schiller's play Die Räuber (The Robbers), was produced in 1957. He composed two operas based on plays by Ödön von Horváth.
In 1957, Klebe succeeded Wolfgang Fortner as docent for the subjects of Composition and Music Theory at the Hochschule für Musik Detmold. He was appointed professor in 1962 and, over the years, taught many students who went on to become well-known composers: Theo Brandmüller,
Peter Michael Braun ,
Hans Martin Corrinth , Matthias Pintscher, and
Lars Woldt .