He studied with Graziano Polidori; he took part in numerous singing competitions, winning the Mozart Competition at the Teatro Lirico in Cagliari and the special prize at the Toti dal Monte competition in Treviso where, after attending the advanced course with the famous mezzo-soprano Regina Resnik, he made his debut in the role of Valentin in Gounod’s Faust.
Viviani works in the most important stages worldwide, such as: Teatro Carlo Felice di Genova, Teatro Lirico di Cagliari, Canadian Opera, San Francisco Opera, Suntory Hall in Tokyo, Palau de les Arts in Valencia, Teatro Real de Madrid, Teatro La Fenice, Teatro alla Scala, Teatro San Carlo, Teatro de la Maestranza in Sevilla, Opéra de Bastille, Wiener Staatsoper, Royal Opera House, Deutsche Oper, Hamburgische Staatsoper, Staatsoper in Berlin.
His vast repertoire includes roles such as Renato (Un ballo in maschera), Simon Boccanegra, Giovanni lo Sciancato (Francesca da Rimini), Barone Scarpia (Tosca), Tonio (Pagliacci), Nabucco, Carlo Gerard (Andrea Chenier), Rodrigo (Don Carlo).
He made his debut at the Gran Teatre del Liceu in the 2014/15 season with La traviata, and has returned with Poliuto (2017/18), La Gioconda (2018/19), and Cavalleria rusticana and Pagliacci (2019/20).