Angelo Cuniberti joined the Congregation of the Consolata missionaries and received on 29 June 1944 the ordination to the priesthood. In 1952, he came as a missionary to Colombia.
Pope John XXIII. appointed him on 18 April 1961 Apostolic Vicar of Florencia and Titular Bishop of Arsinoe in Cypro. The Pope himself gave him on 21 May of the same year, the episcopal ordination; Fulton John Sheen were co-consecrators, Auxiliary Bishop of New York, and Edoardo MCCJ Mason, Vicar Apostolic of El Obeid. He was a Council Father and participated in all sessions of the Second Vatican Council.
On November 15, 1978 Pope John Paul II accepted his resignation early, probably due to clashes with the Roman Curia.
Angelo Cuniberti committed in 1962 for the establishment of a Teachers' Association ( Asociación de Institute Tutores del Caquetá ( Aica ) ) in Caquetá. He also suggested the establishment of the National Agrarian Federation ( Federación Nacional Agraria ) and the National Association of Small Farmers in Colombia ( Asociación Nacional de Usuarios Campesinos de Colombia - Anuc ) and has contributed significantly to allow the organization of cooperatives.
Through his commitment to a public university in Caquetá and thanks to his intervention in 1971 he founded the Instituto Técnico Universitario Surcolombiano ( Itusco ) in Florencia, the forerunner of today's Universidad de la Amazonia.
He also was involved in the organization of civil society in Caquetá and took action against social injustice; he enjoyed a high reputation among the population. He is also the namesake of the Premio Angel Cuniberti, the Institución Educativa Angel Cuniberti and other facilities.