Arutiunian was born in Yerevan, Armenia, in the family of Grigor and Eleonora Arutiunian. His father was a military serviceman. In 1927, Arutiunian became a member of the Yerevan State Conservatory’s children group, then, at age 14, he was admitted to the Conservatory to the studios of Olga Babasyan (piano), and Sergei Barkhudaryan and Vardges Talyan (composition). He graduated from the Music Conservatory of Yerevan on the eve of World War II. After the war he moved to Moscow, where between 1946 and 1948 he participated in the workshops of House of Armenian Culture, studied composition with Genrikh Litinsky. After graduation he returned to Yerevan to teach at the local Conservatory and in 1954 he was appointed artistic director of the Armenian State Philharmony. He was also a member of the Board of the USSR Composers' Union, as well as of the Armenian SSR Composers’ Union.