The orchestra was founded in 1908, as the first Italian orchestra to devote itself exclusively to symphonic repertoire. Bernardino Molinari was the orchestra's first music director, serving from 1912 to 1944. Subsequent music directors included Franco Ferrara (1944–1945), Fernando Previtali (1953–1973), and Igor Markevitch (1973–1975). The orchestra was noted for its recordings of Italian opera for the Decca label with such conductors as Tullio Serafin. Thomas Schippers had been named the next music director to succeed Markevitch, but Schippers died in December 1977, before he could formally assume the post. The music directorship of the orchestra remained vacant until 1983, with the advent of Giuseppe Sinopoli as music director. Sinopoli assisted in restoring the fortunes of the orchestra, and expanded the orchestra's repertoire to include Mahler and Bruckner. Leonard Bernstein was the honorary president of the orchestra from 1983 until 1990.
Antonio Pappano became the orchestra's music director in 2005. With Pappano, the orchestra has recorded commercially for EMI. Currently, Yuri Temirkanov has the title of honorary conductor of the orchestra.