Youri Egorov was born in Kazan, Tatarstan republic, USSR. He studied music at the Kazan Conservatory from the age of 6 until age 17. At the age of 17, in 1971, Youri took 4th Prize in Paris at the Marguerite Long-Jacques Thibaud Competition. He next studied at the Moscow Conservatory. Youri remained at the Moscow Conservatory for six years.
In 1974, Youri won the Bronze Medal at the Tchaikovsky Competition in Moscow. In 1975, he was awarded the 3rd Prize at the Queen Elisabeth International Music Competition Of Belgium.
Being gay, and feeling politically and sexually constrained by the Soviet system, Youri defected from the Soviet Union in 1976 while on a concert tour in Rome, Italy and travelled to Amsterdam where he was to meet Jan Brouwer (1947-1988), his long term partner.
In 1977 Youri participated in the Van Cliburn Competition in Fort Worth, Texas. He became an audience favorite. When he was not chosen as a finalist, some disappointed and angry listeners formed a committee led by American impresario Maxim Gershunoff, to raise money for Egorov equal to the Van Cliburn top prize of $10,000.
In July, 1978, Musical America Magazine selected Youri Egorov as their "Musician of the Month". He made his Carnegie Hall debut on December 16, 1978 once again under the aegis of Gershunoff. The concert was recorded live. Writing for The New York Times, Harold C. Schonberg said Egorov played "...in a free, romantic style, and his approach is quite different from that of so many competition winners."
In August 1979, two of Youri's albums appeared on Billboard Magazine's Best-Selling Classical LP chart. Throughout the 1980s Youri played primarily in Europe. His last American appearance was in Florida in 1986.
Youri was featured in the book "Great Contemporary Pianists Speak for Themselves" compiled by Elyse Mach. In it, he spoke candidly on the topics of rehearsal, pre-concert nervousness, artistic restrictions in Russia, and his homosexuality.
Egorov died at his home in Amsterdam from what was believed to be complications of AIDS. Youri was 33 years old. He had made 14 recordings at the time of his death and several more were awaiting release. He is buried alongside Jan Brouwer at Driehuis Velsen Crematorium, Driehuis, Noord-Holland, Netherlands.