He was born in Budapest, but grew up in Vienna, studying there and in Leipzig under Eusebius Mandyczewski, and, for a brief period, Max Reger. Richard Strauss appointed him to be his assistant at the Berlin Royal Opera before Szell went off to hold a number of conducting posts throughout Europe: in Berlin, Strasbourg (succeeding Otto Klemperer at the Municipal Theatre there), Prague, Darmstadt, Düsseldorf and Glasgow before becoming pricipal conductor of the Berlin Staatsoper (which by now had replaced the Royal Opera) in 1924. In 1930 he made his American debut with the St. Louis Symphony Orchestra.
He was in the USA at the outbreak of World War II, and settled there. From 1942 to 1946 he was a regular conductor at the Metropolitan Opera in New York City. In 1946 he became an American citizen, and that same year took up the post of principal conductor of the Cleveland Orchestra, a post he held until his death in 1970. It is for his work with them that he is best known - he is credited with raising the ensemble to a world-class level.