Armenian was born in Cairo and had his first music lessons there, moving in 1959 to Vienna to study piano with Bruno Seidlhofer. After graduating, he put his musical studies aside and attended the University of London from 1962 to 1965, where he majored in metallurgy. He returned to the Vienna Academy of Music and studied from 1965 to 1969. In 1968, Armenian was one of two finalists at the International Competition for Young Conductors in Besançon, France.
Armenian emigrated to Canada in 1969 to become the assistant conductor of the Atlantic Symphony Orchestra, located in Halifax, Nova Scotia .From 1971 to 1993, he was the Artistic Director and conductor of the Kitchener-Waterloo Symphony. Under Armenian's guidance, the K-W Symphony emerged by the mid-1970s as one of the most vital in Canada.
Armenian made guest-conducting appearances with the Orchestre Symphonique de Québec in 1974, the Toronto Symphony Orchestra and the National Arts Centre Orchestra in 1975, and conducted Wozzeck for the Canadian Opera Company in 1977.
In 1986, he was made a Member of the Order of Canada.