Berberian was born in New York City; his parents were Armenian immigrants. His father was an accomplished oud player, as well as instrument maker, and oud masters of Armenian, Turkish, and Greek heritage frequented his family's home.
He first recorded traditional oud music with violinist Reuben Sarkisian, when a student at Columbia University in the mid-1950s. He subsequently recorded for a variety of labels including MGM, RCA, Roulette, Verve and Mainstream Records.
He expanded beyond the ethnic music market in the mid to late 1960s, decades before "world music" became fashionable, with a series of LPs which explored fusions between traditional Middle Eastern music, psychedelic rock and jazz. These included "Expressions East" (1964), "Music of the Middle East" (1966), and "Middle Eastern Rock" (1969) with guitarist Joe Beck.
Berberian has commanded the respect of musicians worldwide. He has been featured in numerous concerts and dances throughout the USA, Canada and South America, and is one of only a handful of musicians worldwide given the title of Udi (oud master). He now lives in Massachusetts and maintains an active performance schedule.