In the Bolshevik era, he and his mother travelled to Europe, leaving the Soviet Union. Goldovsky studied with Artur Schnabel in Berlin beginning in 1924 and then with Ernő Dohnányi in Budapest beginning in 1924. He gained fluency in several languages, a gift that served him well as a translator of opera in his later career. He moved to Philadelphia in 1930 where his mother taught at the Curtis Institute and where he became a conducting student of Fritz Reiner and later Reiner's assistant. It was under Reiner that his love and training in opera began. According to U.S. immigration records, he was inspected and detained at Ellis Island twice: once in October 1925 for an irregularity with his visa and once in late July 1932 on suspicion that he might be an illegally contracted labourer; both situations were rather quickly resolved and he was permitted to continue by rail to Pennsylvania. Goldovsky moved to Cleveland in 1936 to become assistant to Artur Rodziński, music director of the Cleveland Orchestra. Then he moved again to Boston in 1942, where he became director of the opera department at the New England Conservatory of Music. The same year, he was named director of the opera department at the Tanglewood Music Center in the Berkshires by Serge Koussevitsky, a position he held through 1962. Koussevitsky had become well acquainted with the Goldovsky family in Russia long before their immigration to the USA.