It was founded in 1838, by Ferenc Erkel, as an opera orchestra for the Hungarian Theatre of Pest (later to become the National Theatre). In 1853, the musicians started to hold their own independent concerts, thus forming the country's first concert orchestra. In 1884, the ensemble moved into the new Opera House on Andrássy Avenue, where it has been presided over by such notable music directors as Ferenc Erkel himself, Sándor Erkel, Gustav Mahler, István Kerner, János Ferencsik, Ádám Medveczky and János Kovács. Other great conductors linked to important periods of the orchestra's existence include Egisto Tango, Sergio Failoni, Otto Klemperer, Ervin Lukács, Miklós Erdélyi, Géza Oberfrank, György Győriványi Ráth and Ádám Fischer. Since March 2016, the orchestra has been under the direction of Balázs Kocsár.
The orchestra premiered some of Bartók’s works for the stage and all of Kodály's, as well as operas by Jenő Hubay, Ernő Dohnányi, György Ránki, Sándor Szokolay and János Vajda. Many composers have also conducted the orchestra, including Kodály and Dohnányi themselves, Emil Petrovics and Péter Eötvös, as well as Pietro Mascagni, Ottorino Respighi and Richard Strauss. In addition to accompanying Hungary's most outstanding opera singers, the orchestra has also performed together with international stars like Mario del Monaco, Nicolai Gedda, Luciano Pavarotti, Montserrat Caballé, José Carreras, Cecilia Bartoli, Erwin Schrott, Jonas Kaufmann, Plácido Domingo, Bryn Terfel and René Pape.