Born in Hungary, he moved to Vienna as a child. He studied conducting at the local academy of music with Hans Swarowsky, as well as composition and the piano. He debuted as conductor in 1971 at the Theater an der Wien. He then worked as a repetiteur and conductor at the Wiener Staatsoper (1973–83), and as a guest conductor at the Graz Opera (1979–81). During the editions of the 1978, 1979, and 1983 Salzburg Festival he was the music assistant of such great masters as Karl Böhm, Christoph von Dohnányi, and Herbert von Karajan. In 1983–85 he was the resident conductor of the Hamburg Opera, then a conductor of the Deutsche Oper Berlin (1985–97). In 1988–93 he was the music director of the State Theatre in Brunswick, and in 1992–97 the main conductor of the Flemish Opera in Antwerp and Ghent. Since 1997 he has been the general music director of the Essen Philharmonic; up to 2013 he was also the artistic director of the city’s Aalto-Musiktheater.
He regularly performs as guest conductor at the Vienna State Opera and leading opera houses in Germany (Berlin, Dresden, Hamburg, Munich). He also appears at the Dutch National Opera in Amserdam, the Bilbao Opera, the Paris Opera, the Royal Opera House in London, the Teatro Bellini in Catania, the Teatro Colón in Buenos Aires, the operas of Washington and San Francisco, the Zurich Opera, the Grand Théâtre de Genève, the Niki-Kai Opera in Tokyo, the Teatro dell’Opera di Roma, and the Hungarian State Opera in Budapest. He performs at the music festivals in Montpellier, Aix-en-Provence, Baden-Baden, and Savonlinna. He The performances and concerts he conducted in Berlin, Dresden, Genoa, Hannover, Hamburg, Milan, Munich, Paris, Rome, Turin, Nagoi, Budapest, and Vienna were broadcast on TV.
He recorded operas by Giacomo Puccini, Giuseppe Gazzaniga, and Alexander von Zemlinsky, along with different symphony works. His albums of Alban Berg’s and Hans Werner Henze’s music were nominated for the Grammy and ICMA awards; the performance of Salome he conducted at the Baden-Baden Festival was released on DVD. Under his directorship, Aalto-Musiktheater was named the best opera house of 2008 and the Essen Philharmonic – the best orchestra of 2003 and 2008 by the jury of Opernwelt magazine. Soltesz himself was awarded the honorary citizenship of the Rhur Region in 2009. In 2010 North Rhine-Westphalia granted him a honorary doctorate.