György Kurtág was born on 19 February 1926 at Lugos (Lugoj in Romanian) in the Bánát region of Romania. He has been a Hungarian citizen since 1948; since 2002 he holds Hungarian–French dual citizenship. Kurtág started playing the piano at the age of 5 with Klára Vojkicza-Peia. Music-making with his mother was in subsequent years an important source of inspiration: they played arrangements for piano duet of symphonies by Haydn and Beethoven as well as overtures by Mozart.

The first genuine pedagogue in his life was the piano teacher Magda Kardos at Temesvár/Timişoara who exerted a life-long influence on Kurtág, even in the field of composition. His first teacher of composition (harmony and counterpoint) was Max Eisikovits, also at Temesvár/Timişoara. In September 1945, Kurtág sat for an entrance examination at the Budapest Academy of Music – it was on that occasion that he made the acquaintance of György Ligeti who was to remain his friend until the latter’s death in 2006. Kurtág began his studies at the Budapest Academy of Music in 1946. His professors included Pál Kadosa (piano), Leó Weiner (chamber music), Sándor Veress and subsequently Ferenc Farkas (composition); he also received important impulses from Pál Járdányi. Kurtág obtained his degree in piano and chamber music in 1951, and in composition in 1955.

In 1947, Kurtág married Márta Kinsker who has since been of decisive significance in every field of life: as wife, as the mother of their son, György Kurtág Jr (born in 1954), as pianist and also as the first listener and critic of his compositions in gestation.

In 1957/1958, Kurtág attended the courses of Messiaen and Milhaud in Paris. It was, however, Marianne Stein who made the greatest impact.  Not only did she help him find the way out of the crisis that had paralysed his work as a composer for several years – she also opened a new chapter in his career (“Marianne halved my life”); she showed him a new direction. Hence the dedication of String Quartet Op. 1 and of the Kafka Fragments, Op. 24 to Marianne Stein. During the course of the months in Paris, Kurtág attended concerts of the Domaine musical under the baton of its founder, Pierre Boulez and heard several of Boulez’ compositions – an experience which was to prove of significance for his thinking. The time in Paris as well as the few days in Cologne on his way back to Budapest when he met Ligeti again and heard his electronic composition Artikulation; also the acquaintance with Stockhausen and listening to his Gruppen for three orchestras were further decisive influences which played an important role when he was working on the String Quartet Op. 1.

Between 1960 and 1968, Kurtág acted as répétiteur for soloists of the National Concert Bureau; in 1967, he was invited to teach at the Academy of Music. Initially, he was assistant to Pál Kadosa in piano, later on he taught chamber music.  He retired in 1986 but continued to give classes regularly until 1993. Since then, right up to the present day, he holds courses in chamber music in many European countries as well as in the United States. He and his wife also appear in recitals where they play from the piano series Játékok [Games] alternating with Kurtág’s Bach transcriptions.

In 1971, Kurtág spent a year in West Berlin on a DAAD scholarship. He was awarded the Kossuth Prize in 1973 (in 1996, he was decorated with the prize a second time). In 1981, the Ensemble Intercontemporain played the world premiere in Paris of Messages of the Late Miss R.V.Troussova, Op. 17 for soprano and chamber ensemble (soloist: Adrienne Csengery, conductor: Sylvain Cambreling). It was that event which marked Kurtág’s international breakthrough. In 1993, at the invitation of the Wissenschaftskolleg, he moved to Berlin for two years as composer-in-residence of the Berlin Philharmonic. In 1995–1996 he was a guest of the Konzerthaus in Vienna in the same capacity. There followed Amsterdam (1996–1998), Berlin again (1998–1999) and Paris (1999–2001). Kurtág and his wife have been living at St André de Cubzac near Bordeaux since 2001.

György Kurtág has been decorated with many awards and prizes. They include the Prize of the Ernst von Siemens Music Foundation in 1998 and the Grawemeyer Award – one of the world's most prestigious music prizes – for ...concertante..., Op. 42 in 2006.