The orchestra traces its origins to a concert given by a group of forty musicians in 1900 with conductor Hans Kreissig. It continued to perform and grow in numbers and stature, so that in 1945 it was in a position to appoint Antal Doráti as music director. Under Doráti, the orchestra became fully professional. Several times during the history of the orchestra it has suspended operations, including periods during the First and Second World Wars from 1914 to 1918 and from 1942 to 1945, and more recently in 1974 due to fiscal restraints. Subsequent music directors have included Georg Solti and Eduardo Mata. Andrew Litton was music director from 1992 to 2006. In 2007, Jaap van Zweden was named the DSO's 15th music director, to begin full-time with the 2008-2009 season.
The 2005 recording of the four Rachmaninoff piano concerti and the Rhapsody on a Theme of Paganini with Stephen Hough during live performances has been compared to the recordings by the composer himself. The orchestra was awarded the Gramophone Awards 2005 Editor's Choice; CD of the Week and Record of the Year 2004 from The Sunday Times; and Classical Brit Award 2005 Critics' Choice.