Randazzo was born in the hamlet of Val di Chiesa on the island of Salina, in the Aeolian Islands, Italy. A journalist, he has written for both Italian and Australian daily newspapers, as well as a variety of journals. In Melbourne he was one of the first contributors to the major Italian newspaper Il Globo, founded in 1959. In the early 1970s, he left the paper, returning in 1978 as managing editor. He continued in this position until early 2006. In April 2006, he was elected to the Senate of the Italian Parliament, as an overseas candidate for the centre-left coalition, 'l'Unione'.
He has played an important part in the cultural and political life of Italians in Australia, holding a number of significant positions, such as President of the 'Associazione Eoliani nel Mondo'. He was also co-founder of the 'Compagnia Teatrale Italo-Australiana' (Italo-Australian Theatre Company) in Melbourne, who have performed many of his plays. As well, he was co-founder of ICAIE ('Iniziativa Culturale Australia-Isole Eolie') and 'Famiglia Siciliana', a federation of associations for Sicilians in Victoria. He has received a number of awards, including 'Cavaliere Ufficiale (1980) del'Ordine al Merito della Repubblica Italiana' for 'cultural merit', and the medal for the Centenary of Federation in Australia (2001) for services to the information sector.
His plays have been performed by various Italo-Australian theatre groups and his play, Victoria Market, was workshopped at the National Playwrights' Conference in 1986. He has also translated into Italian The Eureka Stockade by Raffaello Carboni (La Barricata di Eureka (1980)) and History of Australia by Manning Clark (La Storia dell'Australia (1990)).