The orchestra was founded in 1949, with members of an earlier radio orchestra in Munich as the core personnel. Eugen Jochum was the orchestra's first chief conductor, from 1949 until 1960. Subsequent chief conductors have included Rafael Kubelík, the longest serving of the orchestra's chief conductors, as well as Sir Colin Davis and Lorin Maazel. The current principal conductor of the orchestra, since 2003, is Mariss Jansons.
The orchestra participated in the "Musica Viva" concerts, originally founded by the composer Karl Amadeus Hartmann, in its early years.
The orchestra received the 2006 Grammy Award for Best Orchestral Performance for its recording of Shostakovich's 13th Symphony. It was also named the 6th best orchestra in Europe in a survey for Le Monde de la Musique.