Boder was born on November 9, 1958, in Darmstadt. A graduate of the Musikhochschule Hamburg, he went on for further studies in Florence, Italy, with Zubin Mehta and Riccardo Muti. He served as an assistant conductor under Michael Gielen at the Frankfurt Opera, and at just 29, he was named the chief conductor of the Basel Orchestra in Switzerland. During this period, he held guest conductorships at several top German opera houses and at London's Covent Garden (where he made his debut with Verdi's Rigoletto), as well as, slightly later, the San Francisco Opera. His contemporary opera specialty became evident early as he conducted the world premiere of Luca Lombardi's Faust. Un Travestimento at the Basel Opera. It intensified at the Vienna State Opera, where he made the first of many appearances in a performance of Berg's Wozzeck. There he became one of the company's go-to conductors for contemporary music, leading world premieres of Friedrich Cerha's Die Reise vom Steinfeld and Aribert Reimann's Medea (and his Das Schloss as well). He also premiered works by Hans Werner Henze and Krzysztof Penderecki, among others, and he gave the German premiere of George Enescu's Oedipe. Boder also conducted operas of the19th and early 20th centuries in Vienna, including Richard Strauss' Ariadne auf Naxos, Die Frau ohne Schatten, and Elektra. In 2008, Boder became the general music director of the Liceu Theater in Barcelona, remaining in that post until 2012. That year, he was named the chief conductor at the Royal Danish Theatre in Copenhagen.
Boder conducted the Vienna production of Das Schloss for a recording on the Wergo label in 1999, and since then, he has made several recordings of instrumental music. In 2007, he moved to Naxos for a recording of Gloria Coates' Symphony No. 15 with the Vienna Radio Symphony. Boder returned in 2020, leading the ORF Vienna Radio Symphony (as it was by then named) in a recording of orchestral works by Morton Feldman. ~ James Manheim, Rovi