He started writing songs by the age of 10, acted and sang his own composition in Agarwala’s second film, Indramalati (1939). Hazarika obtained a BA and MA in political science at Banaras Hindu University and then worked as a producer for All India Radio’s Guwahati station. He received a scholarship to study in New York where he made a PhD in mass communication at Columbia University. During his time in America, he sang with Paul Robeson and was briefly jailed for participating in civil rights demonstrations. In 1972 and 1973 he sang at East Berlin’s Festival of Political Songs.
He was awarded multiple prizes and honors: the National Film Award for Best Music Direction in 1975, recipient of Sangeet Natak Akademi Award in 1987, Padmashri, Padmabhushan, the Dada Saheb Phalke Award (1992), India’s highest award in cinema and Sangeet Natak Akademi Fellowship, the highest award of the Sangeet Natak Akademi, India’s National Academy for Music, Dance and Drama. Posthumously he was awarded the Padma Vibhushan, India's second-highest civilian award, in 2012.