Klaus Huber was born in Berne on 30 November 1924. He attended high school in Basel and the Küsnacht Teacher-Education School (Kantonsschule Küsnacht). From 1947 to 1949, he attended the Conservatory of Zurich, where he studied violin with Stefi Geyer, as well as music pedagogy. From 1947 to 1955, he remained in Zurich to study composition with his godfather, Willy Burkhard and from 1955 to 1956, studied with Boris Blacher at the Staatliche Hochschule für Musik in Berlin. From 1961 to 1972, he taught at the Basel Musikakademie, which marked the beginning of a long career teaching composition, becoming one of the great teachers of the generation of composers born after 1945. In 1969, he received an artist fellowship from DAAD in Berlin, and succeeded Wolfgang Fortner teaching at the Hochschule für Musik Freiburg, where he remained until his retirement in 1990, training composers such as Brian Ferneyhough, Wolfgang Rihm, and Michael Jarrell.

In 1955, his Sechs kleine Vokalisen premiered in Bilthoven (Holland). In 1959, the premiere of Des Engels Anredung an die Seele at the ISCM World Music Days in Rome brought him international renown; he was awarded first prize in the chamber music composition competition from a jury that included Luigi Dallapiccola and Wladimir Vogel). In 1961, Noctes premiered at the Darmstadt Summer Course, during which Theodor Adorno asked to meet Huber. A portion of his Soliloquia was performed during the ISCM Festival in London in 1962. In the spring of 1968, Huber travelled to the U.S.S.R. with fellow composer Constantin Regamey, then traveled to Nicaragua in 1983, where he met Ernesto Cardenal. That same year, the complete version of Erniedrigt-Geknechtet-Verlassen-Verachtet premiered at the Donaueschinger Musiktage. Huber spent much of 1999 working on his opera Schwarzerde, which premiered in Basel in 2001. Die Seele muss vom Reittier steigen..., premiered in Donaueschingen and in Paris in 2002. In 2003 and 2004, Die Erde tanzt sich auf den Hörnern eines Ochsen was performed in Cairo and in Drochtersen-Huell. In 2004, À l’âme de marcher sur ses pieds de soie... premiered at the Wittener Tagen für Neue Kammermusik. Numerous concerts and events were held to celebrate Huber's eightieth birthday in Germany, Luxemburg, Switzerland, France, and Spain. In 2007, Quod est pax ? – Vers la raison du cœur... premiered at Warsaw Autumn.

Klaus Huber was a guest professor and composer in residence the world over, including Bilthoven (1966, 1968, 1972), McGill University and Brazil (1984), Siena (1985), IRCAM (1986, 1998, 1990, 1993), the Conservatoire de Paris (CNSMDP - 1987, 1989, 1992), Radziejowice (1987), Malmö, Stockholm and the Sibelius Academy (1989), Royaumont (1990, 1996), the Royal Academy of Music and the Conservatoire de Genève (1991), the Brandenburgisches Kolloquium Neue Musik in Berlin, the Musica de Strasbourg Festival, the Basel Musikakademie and the Huddersfield Festival (1992), the Scuola Civica di Musica in Milan (1992, 1993), Centre Acanthes (1993, 2003), the Toronto New Music Concerts (1993), the Lucerne Internationale Musikfestwochen (1994), the Akiyoshidai Festival in Japan (1995), the Conservatoire de Lyon (CNSMDL) and Aigion in Greece (1996), Sarajevo, Bremen and Caracas (1997), Bergen (1998), and Trossingen (2004).

He received many awards and honors, including the Beethoven Prize, the composition prize of the Swiss Musicians' Association, the city of Basel Arts Prize, the Reinhold Schneider Prize, the Prix Italia, the Villa Ichon Culture and Peace Prize (Bremen), the Salzburg Music Prize, the Deutscher Musikautorenpreis (German Music Authors' Prize, in the category Lifetime achievement), and the Ernst von Siemens Music Prize. He was a member of the Bavarian Academy of Fine Arts, the Berlin Academy of Arts, and the Manheim Academy of Arts, as well as an honorary member of the ISCM. He held an honorary doctorate from the University of Salzburg. His scores were published by Ricordi (Munich) starting in 1975, as well as by Schott. His manuscripts are held at the Paul Sacher Foundation archives in Basel. A volume of his collected writings, titled Umgepflügte Zeit, was published in 1999. Klaus Huber died on 2 October 2017 in Perugia, Italy.