Eötvös was born in Székelyudvarhely (now Odorheiv Secviesc), Romania, on January 2, 1944. As a child he studied piano, violin, flute percussion, and by age 11 composed a cantata. At 14, he was accepted at the Budapest Academy of Music to study composition, and by 18, though still a student, he was appointed director of the Budapest Comedy Theater. He was soon composing film scores and conducting various second-tier Hungarian orchestras.
From 1966-1968, he studied conducting at Cologne's Hochschule für Musik. In the latter year he met Stockhausen and over the next decade began performing regularly in the Stockhausen Ensemble. From 1971-1979, he worked on integrating electronic elements into music at Cologne's Westdeutscher Rundfunk. Some of his first important large works date to this period: Harakiri (1973), for narrator and instrumentalists, and Il Maestro (1974), for performer and two pianos. Meanwhile, his career in composition advanced with successful orchestral works like Psychokosmos (1993), based on earlier material; Shadows (1996), which uses electronic amplification; and zeroPoints (1999), which was premiered in London in 2000 by the London Symphony Orchestra under Pierre Boulez. In the new century Eötvös has produced several notable operas: Le Balcon (2002) and Angels in America (2002-2004). Eötvös has been active in the recording studio, leading many of his own works, mostly on the Budapest-based label BMC, but also on DG, BIS, and Hungaroton.