Avetisyan was born in Leninakan, Armenian SSR (now Gyumri, Armenia). He graduated from the Yerevan State Musical Conservatory where he studied composition with professor Edvard Mirzoyan. At age 25 he was the first Armenian composer honored with gold medals in the Berlin and Moscow international competitions. In addition to his studies in classical music, Avetisyan became an authority in Armenian folk music and traditional instruments, especially the kanun. He composed the first Concerto for Kanun and Symphony Orchestra in 1954. Avetisyan dedicated his creative life to researching and developing the performance practice of the Armenian folk music.
Avetisyan founded the Folk Music Department of the Komitas National Conservatory in 1978 where, under his guidance, an entire generation of master instrumentalists were trained. He created numerous famous songs, ballet, oratorio, film and dance music, as well as a large number of works for various folk instruments. His brilliant melodic work reveal a refined lyricism. In 1958 he assumed the role of the artistic director of National Dance Ensemble, and later, the Tatoul Altunian Song and Dance Ensemble, where his new folk instrumental and vocal music became a staple of the repertory.
He married Armenian folk dancer Sona Avetisyan. His son Dr. Mikael Avetisyan is the former conductor of Armenian Philharmonic Orchestra, Yerevan State Symphony Orchestra and guest conductor with many European orchestras, he is currently Music Director of the Armenian Society of Los Angeles Choir.