The orchestra dates back to 1548, when Dresden was part of the Holy Roman Empire; it was founded by the Elector Moritz of Saxony to accompany the court chorus in the new large choral compositions of the time. It evolved from an even older group, the Kurfürstlich-Sächsische und Königlich-Polnische Kapelle. During the 17th century, its music directors included Heinrich Schütz and Michael Praetorius. As opera grew at the Dresden court, one of the orchestra's main functions was to accompany the leading German opera company of the day, and Johann Adolf Hasse was the music director or Kapellmeister from 1734 to 1763. The orchestra and opera persisted through the unrest of late 18th century Europe, emerging as an operatic center under Carl Maria von Weber in the early Romantic era. Other famous names to conduct the orchestra in opera were Richard Wagner, who called it a "magic harp" and premiered Rienzi, Die fliegende Holländer, and Tannhäuser there, and, later, Richard Strauss.
The orchestra's recording catalog is large, including multiple releases almost every year since 1990 on such labels as Berlin Classics, Denon, and Deutsche Grammophon. In 2017 the orchestra under Thielemann released a recording of Bruckner's Symphony No. 4 in E flat major ("Romantic") on the Hänssler label. Many of its historical performances have also been remastered and re-released. In the 21st century, the orchestra has also begun a composers-in-residence program; holders of position have included Hans Werner Henze, Sofia Gubaidulina (twice), Wolfgang Rihm, and, in 2017-2018, Arvo Pärt.