He performed at the Metropolitan Opera as Siegfried, conducted by James Levine and alongside Hildegard Behrens as Brünnhilde, resulting in a recording that won a Grammy Award.

After his voice was discovered when he performed at a private birthday celebration, he studied singing at the Hochschule für Musik Carl Maria von Weber in Dresden with Schellenberg.

[1] Goldberg made his debut in 1966 at the Sächsische Landesbühne in Radebeul in a small role in Mozart's Die Zauberflöte, and later appeared there as Luigi in Puccini's Il tabarro.

[4][5] His roles at the house included Beethoven's Fidelio; Weber's Max in Der Freischütz and Hüon in Oberon; Wagner's Tannhäuser; Lohengrin, Erik, and Stolzing in Die Meistersinger von Nürnberg; Siegfried and Parsifal; Gounod's Faust; Don José in Bizet's Carmen; Alfredo in Verdi's La traviata; Hermann in Tchaikovsky's Pique Dame; Sergei in Shostakovitch's Katerina Ismailowa; Stewa in Janáčeks Jenufa; and Pedro in d'Alberts Tiefland.

His roles in Richard Strauss' operas included Bacchus in Ariadne auf Naxos; the Emperor in Die Frau ohne Schatten; Herod in Salome; and Ägisth in Elektra.

[3] He also performed as Stolzing for his debut with the Royal Opera House in London in 1982,[2] and appeared as Florestan in Fidelio at the Salzburg Festival the same year,[2] alongside Éva Marton in the title role, and conducted by Lorin Maazel.

Jürgen Kesting from the FAZ wrote that "he still sings the role gloriously: with the beautiful tone demanded by Schönberg, good connections and smooth transitions, overcoming expressive resistances especially in moments of highest tension, sometimes with refined parlando.

Also in 2015, Barenboim had the idea of casting great Wagner singers of previous years as the various Masters in Die Meistersinger von Nürnberg; Goldberg performed as Eisslinger,[11] and reprised it in 2019, alongside Franz Mazura as Schwarz, at age 95.

[4][15] Goldberg achieved attention when he sang the role of Wagner's Parsifal for a 1982 opera film directed by Hans-Jürgen Syberberg, while two actor perform the action; his singing was described as "with a youthful radiance that is precisely that of the chaste madman", conducted by Armin Jordan.