Ligeti was born in 1923 at Dicsőszentmárton (which was renamed Târnăveni in 1941), in the Romanian region of Transylvania to Dr. Sándor Ligeti and Dr. Ilona Somogyi. His family was Hungarian Jewish. He was the grandnephew of the Violinist Leopold Auer and cousin of Hungarian Philosopher Ágnes Heller.

In 1941 Ligeti received his initial musical training at the conservatory in Cluj, and during the summers privately with Pál Kadosa in Budapest. 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-Gusen concentration camp and both of his parents were sent to Auschwitz. His mother was the only other survivor of his immediate family.

Many of Ligeti's very earliest works were written for chorus and included settings of folk songs. His largest work in this period was a graduation composition for the Budapest Academy, entitled Cantata for Youth Festival, for four vocal soloists, chorus and orchestra. One of his earliest pieces now in the repertoire is his Cello Sonata, a work in two contrasting movements that were written in 1948 and 1953 respectively. It was initially banned by the Soviet-run Composer's Union and had to wait a quarter of a century before its first public performance.

Following World War II, 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. However, after a year he returned to Franz Liszt Academy in Budapest, this time as a Teacher of harmony, counterpoint and musical analysis, a position he secured with the help of Kodály and held between 1950 and 1956. As a young Teacher, Ligeti took the unusual step of regularly attending the lectures of an older colleague, the Conductor and musicologist Lajos Bárdos, a conservative Christian whose circle represented for Ligeti a safe haven, and whose help and advice he later acknowledged in the prefaces to his own two harmony textbooks (1954 and 1956). 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 Eastern Bloc.

Because of Soviet censorship, his most daring works from this period, including Musica ricercata and his String Quartet No. 1 Métamorphoses nocturnes (1953–1954), were written for the 'bottom drawer'. Composed of a single movement divided into seventeen contrasting sections linked motivically, the First String Quartet is Ligeti's first work to suggest a personal style of composition. The string quartet was not performed until 1958, after he had fled Hungary for Vienna.

Shortly after its composition, Ligeti arranged six of the movements of Musica ricercata for wind quintet under the title 'Six Bagatelles for Wind Quintet'. The Bagatelles were performed first in 1956, but not in their entirety: the last movement was censored by the Soviets for being too 'dangerous'.

Ligeti's music appears to have been subsequently influenced by his electronic experiments, and many of the sounds he created resembled electronic textures. Ligeti coined the term "micropolypony" to describe the texture of the second movement of Apparitions (1958–59) and Atmosphères (1961). This texture is a similar to that of polyphony, except that the polyphony is obscured in a dense and rich stack of pitches. Micropolyphony can be used to create the nearly static but slowly evolving works such as Atmosphères in which the individual instruments become hidden in a complex web of sound. According to Ligeti, after Apparitions and Atmosphères, he "became famous".

Ligeti has been described as "together with Boulez, Berio, Stockhausen, and Cage as one of the most innovative and influential among progressive figures of his time". From about 1960, Ligeti's work became better known and respected. His best-known work was written during the period from Apparitions to Lontano, which includes Atmosphères, Volumina, Aventures and Nouvelles Aventures, Requiem, Lux Aeterna, and his Cello Concerto; as well as his opera Le Grand Macabre. In recent years, his three books of piano études have also become well known and are the subject of the Inside the Score project of Pianist Pierre-Laurent Aimard,

With Volumina (1961–62, revised 1966) for solo organ, Ligeti continued with clusters of notes, translated into blocks of sound. In this piece, Ligeti abandoned conventional music notation, instead using diagrams to represent general pitch areas, duration, and flurries of notes.

Aventures (1962), like its companion piece Nouvelles Aventures (1962–65), is a composition for three Singers and instrumental septet, to a text (of Ligeti's own devising) that is without semantic meaning. In these pieces, each singer has five roles to play, exploring five areas of emotion, and they switch from one to the other so quickly and abruptly that all five areas are present throughout the piece.

Requiem (1963–65) is a work for Soprano and mezzo-soprano soloists, twenty-part chorus (four each of Soprano, mezzo-soprano, alto, tenor, and bass), and orchestra. Though, at about half an hour, it is the longest piece he had composed up to that point, Ligeti sets only about half of the Requiem's traditional text: the "Introitus", the "Kyrie" (a completely chromatic quasi-fugue, where the parts are a montage of melismatic, skipping micropolyphony), and the "Dies irae"—dividing the latter sequence into two parts, "De die judicii" and "Lacrimosa".

Ligeti's Cello Concerto (1966), which is dedicated to Siegfried Palm, is composed of two movements: the first begins with an almost imperceptible cello which slowly shifts into static tone clusters with the orchestra before reaching a crescendo and slowly decaying, while the second is a virtuoso piece of dynamic atonal melody on the part of the cello.

Lontano (1967), for full orchestra, is another Example of micropolyphony, but the overall effect is closer to harmony, with complex woven textures and opacity of the sound giving rise to a harmonious effect. It has become a standard repertoire piece.

Ramifications (1968–69), completed a year before the Chamber Concerto, is scored for an ensemble of strings in twelve parts—seven violins, two violas, two cellos and a double bass—each of which may be taken by one player or several. The twelve are divided into two numerically equal groups but with the instruments in the first group tuned approximately a quarter-tone higher (four violins, a viola and a cello). As the group play, the one tuned higher inevitably tends to slide down toward the other, and both get nearer each other in pitch.

In the Chamber Concerto (1969–70), several layers, processes and kinds of movement can take place on different planes simultaneously. In spite of frequent markings of "senza tempo", the instrumentalists are not given linear freedom; Ligeti insists on keeping his texture under strict control at any given moment. The form is like a "precision mechanism". Ligeti was always fascinated by machines that do not work properly and by the world of Technology and automation. The use of periodic mechanical noises, suggesting not-quite-reliable machinery, occurs in many of his works. The scoring is for flute (doubling piccolo), oboe (doubling oboe d'amore and cor anglais), clarinet, bass clarinet (doubling second clarinet), horn, trombone, harpsichord (doubling Hammond organ), piano (doubling celesta), and solo string quintet.

From the 1970s, Ligeti turned away from sonorism and began to concentrate on rhythm. Pieces such as Continuum (1968) and Clocks and Clouds (1972–73) were written before he heard the music of Steve Reich and Terry Riley in 1972. But the second of his Three Pieces for Two Pianos (1976), entitled "Self-portrait with Reich and Riley (and Chopin in the background)", commemorates this affirmation and influence. During the 1970s, he also became interested in the polyphonic pipe music of the Banda-Linda tribe from the Central African Republic, which he heard through the recordings of one of his students.

In 1973 Ligeti became professor of composition at the Hamburg Hochschule für Musik und Theater, eventually retiring in 1989. While living in Hamburg, his wife Vera remained in Vienna with their son, Lukas, who later became a Composer.

In 1977, Ligeti completed his only opera, Le Grand Macabre, thirteen years after its initial commission. Loosely based on Michel de Ghelderode's 1934 play, La balade du grand macabre, it is a work of Absurd theatre—Ligeti called it an "anti-anti-opera"—in which Death (Nekrotzar) arrives in the fictional city of Breughelland and announces that the end of the world will occur at midnight. Musically, Le Grand Macabre draws on techniques not associated with Ligeti's previous work, including quotations and pseudo-quotations of other works and the use of consonant thirds and sixths.

After Le Grand Macabre, Ligeti struggled for some time to find a new style. Besides two short pieces for harpsichord, he did not complete another major work until the Trio for Violin, Horn and Piano in 1982, over four years after the opera. His music of the 1980s and 1990s continued to emphasise complex mechanical rhythms, often in a less densely chromatic idiom, tending to favour displaced major and minor triads and polymodal structures. During this time, Ligeti also began to explore alternate tuning systems through the use of natural harmonics for horns (as in the Horn Trio and Piano Concerto) and scordatura for strings (as in the Violin Concerto). Additionally, most of his works in this period are multi-movement works, rather than the extended single movements of Atmosphères and San Francisco Polyphony.

Lux Aeterna was used again in Peter Hyams's 1984 sequel to 2001, 2010.

From 1985 to 2001, Ligeti completed three books of Études for piano (Book I, 1985; Book II, 1988–94; Book III, 1995–2001). Comprising eighteen compositions in all, the Études draw from a diverse range of sources, including gamelan, African polyrhythms, Béla Bartók, Conlon Nancarrow, Thelonious Monk, and Bill Evans. Book I was written as preparation for the Piano Concerto, which contains a number of similar motivic and melodic elements. Ligeti’s music from the last two decades of his life is unmistakable for its rhythmic complexity. Writing about his first book of Piano Etudes, the Composer claims this rhythmic complexity stems from two vastly different sources of inspiration: the Romantic-era piano music of Chopin and Schumann and the indigenous music of sub-Saharan Africa.

In 1988, Ligeti completed his Piano Concerto, a work which he described as a statement of his "aesthetic credo". Initial sketches of the Concerto began in 1980, but it was not until 1986 that he found a way forward and the work proceeded more quickly. The Concerto explores many of the ideas worked out in the Études but in an orchestral context.

Invited by Walter Fink, he was the first Composer featured in the annual Komponistenporträt of the Rheingau Musik Festival in 1990.

In 1993, Ligeti completed his Violin Concerto after four years of work. Like the Piano Concerto, the Violin Concerto uses the wide range of techniques he had developed up until that point as well as the new ideas he was working out at the moment. Among other techniques, it uses a passacaglia, "microtonality, rapidly changing textures, comic juxtapositions... Hungarian folk melodies, Bulgarian dance rhythms, references to Medieval and Renaissance music and solo violin writing that ranges from the slow-paced and sweet-toned to the angular and fiery."

Other notable works from this period are the Viola Sonata (1994) and the Nonsense Madrigals (1988–93), a set of six a cappella compositions that set English texts from william Brighty Rands, Lewis Carroll, and Heinrich Hoffman. The third Madrigal is a setting of the English alphabet.

Ligeti's last works were the Hamburg Concerto for solo horn, four natural horns and chamber orchestra (1998–99, revised 2003, dedicated to Marie Luise Neunecker), the song cycle Síppal, dobbal, nádihegedüvel ("With Pipes, Drums, Fiddles", 2000), and the eighteenth piano étude "Canon" (2001). Additionally, after Le Grand Macabre, Ligeti planned to write a second opera, first to be based on Shakespeare's The Tempest and later on Carroll's Alice's Adventures in Wonderland, but neither came to fruition.

Ligeti's music is best known to the general public for its use in three films of Stanley Kubrick's, which gained him a world-wide audience. The Soundtrack to 2001: A Space Odyssey includes excerpts from four of his pieces: Atmosphères, Lux Aeterna, Requiem and Aventures. Atmosphères is heard during the "Star Gate" sequence, with portions also heard in the Overture and Intermission. Lux Aeterna is heard in the moon-bus scene en route to the Tycho monolith. The Kyrie sequence of his Requiem is heard over the first three monolith encounters. An electronically altered version of Aventures, unlisted in the film credits, is heard in the cryptic final scenes. The music was used, and in some cases modified, without Ligeti's knowledge, and without full copyright clearance; when the film came to Ligeti's attention, he "successfully sued for having had his music distorted", but settled out of court. Kubrick in return sought permission and compensated Ligeti for use of his music in later films.

Ligeti's health deteriorated after the turn of the millennium and he died in Vienna on 12 June 2006 at the age of 83. Although it was known that he had been ill for several years and had used a wheelchair for the last three years of his life, his family declined to release details of his cause of death.

Ligeti is also known to the public through the use of his music in other films by other Directors. Lontano was also used in Martin Scorsese's 2010 psychological thriller film Shutter Island. The first movement of the Cello Concerto was used in the Michael Mann 1995 crime film Heat. The Requiem was used in the 2014 film Godzilla. The Cello Concerto and the Piano Concerto were used in Yorgos Lanthimos' 2017 film The Killing of a Sacred Deer.

On the other hand, the later music—and a few earlier pieces such as Continuum—treats the pulse as a musical atom, a Common denominator, a basic unit, which cannot be divided further. Different rhythms appear through multiplications of the basic pulse, rather than divisions: this is the principle of African music seized on by Ligeti. It also appears in the music of Philip Glass, Steve Reich and others; and significantly it shares much in Common with the additive rhythms of Balkan folk music, the music of Ligeti’s youth. He described the music of Conlon Nancarrow, with its extremely complex explorations of polyrhythmic complexity, as "the greatest discovery since Webern and Ives... something great and important for all music history! His music is so utterly original, enjoyable, perfectly constructed, but at the same time emotional... for me it's the best music of any Composer living today."

The difference between the earlier and later pieces lies in a new conception of pulse. In the earlier works, the pulse is something to be divided into two, three and so on. The effect of these different subdivisions, especially when they occur simultaneously, is to blur the aural landscape, creating the micropolyphonic effect of Ligeti’s music.