István Kovács began his studies at the Ferenc Liszt Music School in his home town of Pécs, and then continued them in Zürich with László Polgár and in Venice with Sherman Lowe. Between 1997 and 1999, he won first prize at the Schubert and the Music of the 20th Century Festival held in Graz, the prize for best singer in the oratorio category at the Francesco Vinas International Singing Competition in Barcelona, the special sponsor's prize at the ARD Competition in Munich, and third prize at the Mozart Competition in Salzburg. Since the 1999/2000 season, he has sung, among others, the roles of Ali (L’italiana in Algeri) and Raimondo (Lucia di Lammermoor) at the Teatro Regio in Turin and Don Giovanni, Sparafucile (Rigoletto) and Nanni (Haydn's L'infedeltá delusa) at the Hungarian State Opera, as well as those of Publio (La clemenza di Tito) in Strasburg, Angelotti (Tosca) in Frankfurt and Timur (Turandot) at Berlin's Staatsoper under den Linden. He has also made a name for himself as a concert singer, performing works by Mozart, Handel, Bartók, Haydn and Bach. In 2004, Hungarian Television recorded his portrayal of the title character in Béla Bartók's Bluebeard's Castle, a role he has also sung in Palermo, Bologna, Tokyo, Stavanger, Budapest and Toulouse, and more recently in Nice, Dortmund and Osaka. In 2013 he sang, to great acclaim, the role of Don Silva (in Verdi's Ernani) with the Bavarian Radio Symphony Orchestra. The 2014/15 season saw him singing the King of Egypt (Aida), Sarastro (The Magic Flute) and Walter (Luisa Miller) back in Budapest, where he also performed in Mendelssohn's oratorio Elijah.
In 2019, in recognition of her outstanding achievements, he was decorated with the Knight's Cross of the Hungarian Order of Merit (civilian division). He received the Gusztáv Oláh Commemorative Plaque in 2022 and he was awarded the Chamber Singer of the Hungarian State Opera in 2023.