Born in Prague, Swoboda studied philosophy in his native city and spent his early career there as a stage actor during the 1820s and 1830s.
On 22 December 1837 he created the role of the Marquis de Chateauneuf in Albert Lortzing's Zar und Zimmermann in Leipzig.
In the 1840–1841 season in Düsseldorf he appeared opposite his wife, dramatic soprano Angelika Peréchon-Swoboda, under the stage name Joseph Nork.
He also appeared as a guest artist during these years in theatres throughout Germany and in Prague, and was frequent performer at the Theater in der Josefstadt in Vienna.
He left that position in 1875 to take over the general management of the Deutsches Theater Budapest with his son Albin serving as artistic director.