Jouri Airapetian was born in Yerevan, Armenia. From 1941 to 1951 he studied at the Yerevan School of Music, in the class of R.K.Andriasyan. He continued his studies at the Yerevan State Conservatory. In 1956 he graduated from the Moscow State Conservatory (Y.V.Flier's class) with excellence, and in 1960 he did his graduate program in the same professor's class.
Jouri Airapetian started teaching in 1961. He has been an Associate Professor since 1973 and has been teaching at the Yerevan State Conservatory since 1978. He was the Dean of its piano faculty from 1977 to 1994. In 1979 he received an academic degree of a Professor. Since 1960 he has maintained close creative relations with the Moscow State Conservatory. He headed the State Examinations Commission at the Moscow Conservatory from 1987 to 1992. Since 1985 Jouri Airapetian has taught master classes in cities across Russia and other countries such as France, Yugoslavia and South Korea.
In 2004 he was awarded a Movses Khorenatsi Medal (RA) for his achievements in performing and for his teaching activities. He is a winner of the Fifth World Festival of Youth and Students in Warsaw (the 2nd Prize, 1955) and such international competitions as Franz Liszt (the 4th prize, 1956) and Queen Elisabeth (1960).
Since 1982 Jouri Airapetian has been a jury member of a number of international competitions held in Moscow, St Petersburg, Bucharest, as well as cities in Latvia and other countries.