Ligeti was born in Dicsőszentmárton, which was renamed Târnăveni in 1945, in Transylvania to a Hungarian Jewish family. Ligeti recalls that his first exposure to languages other than Hungarian came one day while listening to a conversation among the Romanian-speaking town police. Before that he hadn't known that other languages existed. He moved to Cluj (Kolozsvár) with his family when he was 6, and he was not to return to the town of his birth until the 1990s.
Ligeti received his initial musical training at the conservatory in Cluj, and during the summers privately with Pál Kadosa in Budapest.
In 1940, Northern Transylvania was occupied by Hungary following the Second Vienna Award. In 1944, Ligeti's education was interrupted when he was sent to a forced labor brigade by the Horthy regime. His brother, age 16, was deported to the Mauthausen concentration camp, and both of his parents were sent to Auschwitz. His mother was the only other survivor of his immediate family.
Following the war, Ligeti returned to his studies in Budapest, Hungary, graduating in 1949 from the Franz Liszt Academy of Music. He studied under Pál Kadosa, Ferenc Farkas, Zoltán Kodály and Sándor Veress. He went on to do ethnomusicological research into the Hungarian folk music of Transylvania, but after a year returned to his old school in Budapest, this time as a teacher of harmony, counterpoint and musical analysis. However, communications between Hungary and the West by then had become difficult due to the restrictions of the communist government, and Ligeti and other artists were effectively cut off from recent developments outside the Soviet bloc.
In December 1956, two months after the Hungarian revolution was violently suppressed by the Soviet Army, Ligeti fled to Vienna with his ex-wife Vera (soon to be wife again) and eventually took Austrian citizenship (in 1968). He would not see Hungary again until he was invited to judge a competition in Budapest fourteen years later. On his journey to Vienna, he left most of his Hungarian compositions in Budapest, some of which are now lost; he only took what he considered to be his most important compositions. He later explained, "I considered my old music of no interest. I believed in twelve-tone music!"
A few weeks after arriving in Vienna, he left for Cologne. There he met several key avant-garde figures and learned more contemporary musical styles and methods. These included the composers Karlheinz Stockhausen and Gottfried Michael Koenig, both then working on groundbreaking electronic music. During the summer, he attended the Internationale Ferienkurse für Neue Musik in Darmstadt. Ligeti worked in the Cologne studio with Stockhausen and Koenig and was inspired by the sounds he heard there. However, he produced little electronic music of his own, instead concentrating on instrumental works which often contain electronic-sounding textures.
After about three years, he finally fell out with the Cologne school, because it was too dogmatic and there was a huge amount of factional in-fighting: "There were a lot of political fighting because different people, like Stockhausen, like Kagel wanted to be first. And I, personally, have no ambition to be first or to be important."
Starting around 1960, Ligeti's work became better-known and respected. His best-known work include works in the period from Apparitions (1958–59) to Lontano (1967) and his opera Le Grand Macabre (1978). In recent years, his three books of Études for piano (1985–2001) have become better-known through recordings by Pierre-Laurent Aimard, Fredrik Ullén, and others.
In 1973, Ligeti became professor of composition at the Hamburg Hochschule für Musik und Theater, eventually retiring in 1989. In the early 1980s, he tried to find a new stylistic position (closer to "tonality"), leading to an absence from the musical scene for several years until he reappeared with the Trio for Violin, Horn and Piano (1982). His output was prolific through the 1980s and 1990s. Invited by Walter Fink, he was the first composer featured in the annual Komponistenporträt of the Rheingau Musik Festival in 1990.
However, health problems became severe after the turn of the millennium. On June 12, 2006, Ligeti died in Vienna at the age of 83. Although it was known that Ligeti had been ill for several years and had used a wheelchair the last three years of his life, his family declined to release the cause of his death. Ligeti's funeral was held at the Vienna Crematorium at the Zentralfriedhof, the Republic of Austria and the Hungary Republic of Hungary represented by their respective cultural affairs ministers. The ashes were finally buried at the Zentralfriedhof in a grave dedicated to him by the City of Vienna