La Monte Young grew up in a poor, rural setting. His father was a sheep-herder, and the family lived in a log cabin in a Mormon hamlet in Bear Lake County, Idaho. As a child, Young learned cowboy songs and the basics of the guitar from his aunt, and, at the age of seven, basic music theory and alto saxophone from his father and great uncle, the latter of which was the leader of a brass band. In 1949, after having moved several times, his family settled in Los Angeles.

From 1950 to 1953, Young attended John Marshall High School, where he studied music theory with Clyde Sorenson. He also studied clarinet with William Green (1951-1954) at the Los Angeles Conservatory. He developed a passion for jazz, which he performed in his school's dixieland group. In 1953, he began studies of counterpoint and composition with Leonard Stein, disciple and assistant of Schoenberg, at Los Angeles City College. At this time, he composed works inspired by serialism, including Five Small Pieces for String Quartet (1956). He also became more active in jazz, playing with, among others, Don Cherry, Ornette Coleman and Billy Higgins.

In January 1957, he began studying music theory, counterpoint, and ethnomusiclogy at UCLA, graduating with a Bachelor of Arts in June 1958. He slowly distanced himself from jazz, dedicating most of his time to composing. In 1958, he composed Trio for Strings which, due to its long held notes and spare writing, may be considered the first music work of minimalism. Entering Berkeley University in 1958, Young continued his studies of composition with Seymour Shifrin, Charles Cushing, and William Denny, and analysis with Andrew Imbrie. At this time, he also became friends with Terry Riley.

In the summer of 1959, Young attended the composition seminar of Karlheinz Stockhausen at the Darmstadt Summer Course. This experience notably introduced Young to the techniques and music of John Cage. In the summer of 1960, Young taught composition with Terry Riley at the Anna Halprin Summer Choreography Academy in Marin County, CA. He composed works and performance pieces for "friction sounds" (various objects rubbed against different surfaces), e.g., Poem for Chairs, Tables, Benches, etc. (1960), in which the performers drag furniture across the floor.

In the Autumn of 1960, Young moved to New York, where he quickly acquainted himself with the "downtown" scene. He composed the repetitive work Arabic Numeral (Any Integer) to H.F. (1960), as well as the fifteen Compositions 1960 which are considered to be among the first examples of conceptual art. In 1963, he married visual artist Marian Zazeela. The couple moved into one of the first Downtown artists' lofts, where Young founded The Theater of Eternal Music, an ensemble dedicated to his own music. He composed The Four Dreams of China, an evolutive work of long drones over which he improvised on saxophone.

In 1964, Young began work on two pieces which are still in progress: The Tortoise, His Dreams and Journeys and The Well-Tuned Piano, which were his main focus throughout the 1970s and 1980s. In August 1966, Young began work on a treatise of the theory of just intonation, The Two Systems of Eleven Categories, which remains unfinished and unpublished to this day. He abandoned the saxophone in favour of the voice, which he found to be better suited to just intonation, and frequently performed alone or as a duo with Zazeela.

From 1969 to 1975, the couple toured Europe and the USA annually. Together, they conceived "sound and light environments", known as Dream Houses, which were set up in museums, art galleries, and elsewhere, including at the Maeght Fondation (1970), Documenta 5 in Kassel, the Munich Olympic Games (1972), Contemporanea 5 in Rome, the University of Illinois (1973), and at The Kitchen in New York City (1974).

In 1970, Young and Zazeela embarked upon a period of intense study of Indian music, becoming disciples of vocal virtuoso Pandith Pran Nath. They helped him emigrate to the USA and devoted much of their time and energy to him until Nath's death in 1996. With their guru, Young and Zazeela performed a number of concerts of Indian music together, and explored the practice of raga in their group the Just Alap Raga Ensemble.

From 1979 to 1985, with support from the Dia Foudation, Young and Zazeela moved into the former New York Trade Exchange building on Harrison Street, in which they set up a Dream House which remained open for six years. These premises also served as a research centre and archive of their performances and concert programmes. In 1980, Young composed The Subsequent Dreams of China, and in 1985, Orchestral Dreams.

From 1990, La Monte Young once again participated in a number of collaborative projects. He toured Europe and the USA for two years with The Forever Bad Blues Band and Big Band, widely performing his work Young’s Dorian Blues in A. Also in 1990, he composed Chronos Kristalla, a commission from the Kronos Quartet. Meanwhile, the Dream Houses continued to evolve according to the means at hand; in 1993, with support from the Mela Foundation, Young and Zazeela created Dream House: Seven Years of Sound and Light, an installation which was to remain in place for seven years. Another Dream House, created in 2009 for the Third Mind exhibition at the Guggenheim Museum in New York, was open to the public for a more modest period of four months.