Nørgård is also a prolific writer. He has written many articles dealing with music not only from a technical but also a philosophical viewpoint. His thoughts on the philosophy of music are among the best documented of any composer.
Nørgård was born in Gentofte. He decided that he wanted to become a composer in 1949 after writing a piano sonata. The same year he began studying privately with Vagn Holmboe. He then enrolled at the Royal Danish Academy of Music in Copenhagen from 1952 to 1955.
Nørgård subsequently studied with Nadia Boulanger in Paris from January 1956 to May 1957. During this time he attended the concerts organized by Pierre Boulez, but was vexed by the serialism dominant at the time.
After completing his studies, Nørgård was attached as a lecturer to the Funen Academy of Music in Odense in 1958, a post he retained until 1961. In 1960 he also began to lecture at the Royal Danish Academy of Music. He also worked as a music critic for the newspaper Politiken from 1958 to 1962.
In 1960 Nørgård attended the ISCM World Music Days in Cologne with several other young Danish composers. As the strict serialism of the 1950s was giving way to new avant-garde trends, Nørgård was intrigued by the possibilities of works such as György Ligeti's Apparitions and Pierre Boulez' Pli selon pli. After returning to Denmark he formed a study group with his colleagues.
To begin with, he was strongly influenced by the Nordic styles of Jean Sibelius, Carl Nielsen and Vagn Holmboe. In the 1960s, Nørgård began exploring the modernist techniques of central Europe, eventually developing a serial compositional system based on the "infinity series", which he used in his Voyage into the Golden Screen, Symphony No. 2 and Symphony No. 3, and many of his other works of the late 1960s and 70s. Later he became interested in the Swiss artist Adolf Wölfli, who inspired many of Nørgård's works, including the 4th symphony, the opera Det Guddommelige Tivoli and Papalagi for solo guitar.
Nørgård has composed works in all major genres: six operas, two ballets, six symphonies and other pieces for orchestra, several concertos, choral and vocal works, an enormous number of chamber works, ten string quartets and several solo instrumental works. These include a number of works for the guitar, mostly written for the Danish guitarist Erling Møldrup: In Memory Of... (1978), Papalagi (1981), a series of suites called Tales from a Hand (1985-2001), Early Morn (1997-8) and Rondino Amorino (1999). One of his most important works for percussion solo is I Ching (1982) for the Danish percussionist Gert Mortensen. He has also composed music for several films, including The Red Cloak (1966), Babette's Feast (1987), and Hamlet, Prince of Denmark (1993).