Dvorský studied under Ida Černecká at the Bratislava State Conservatory. There he also enjoyed his first successes at the Slovak National Theatre, making his professional opera debut there in 1972 as Lensky in Tchaikovsky’s Eugene Onegin. He won the national singing contest named after Mikuláš Schneider-Trnavský at Trnava in 1973, and in 1974 he won the first prize at the international Tchaikovsky Competition in Moscow. In 1975, he won first place in the singing contest at the Geneva International Music Competition which led to a yearlong apprenticeship under Renata Carosia and Giuseppe Lugga at La Scala in Milan.
In the following years, he quickly achieved international fame. He debuted at the Vienna State Opera, where he was particularly successful and popular, in 1976, at the New York Metropolitan Opera in 1977, and one year later at La Scala, Milan.
Dvorský was highly esteemed by Luciano Pavarotti, who referred to him several times as, “my legitimate successor”. In these years he became one of the leading tenors worldwide. He received several distinctions, among others being a national artist and state prize-winner of the former Czechoslovakia. Since 2006, Dvorský has been the head of the opera house in Košice, then of the opera house of the Slovak National theater (SND) in Bratislava.