Leopold's adoptive father, Louis Passinock, promoted his fame as a Wunderkind. To forestall his exploitation, a banker named Feinberg offered to finance his study at the Hochschule für Musik in Berlin. Leopold studied under Ernst Rudorff, but could only take three months of regimentation. He, his mother, and his "uncle" Passinock went to New York where he began to concertize at the age of thirteen. They booked him onto a tour of the West that eventually went bust, stranding the boy, who worked his way back to New York.
Again, a wealthy arts patron sought to "rescue" him. Leon Saxe arranged for him to go to Europe to study with the virtuoso Franz Liszt. By the time Leopold's ship reached Europe, Liszt was dead. But Camille Saint-Saëns, who had lost his children, became a mentor, mostly discussing interpretation and other esthetic manners. Godowsky had some success in Europe, but not enough to satisfy him, and returned to America. There he had a career as a respected piano teacher in New York, Philadelphia, and Chicago. He developed the modern approach to piano playing, emphasizing economy of motion and release of weight (rather than direct muscle power) as the basis for playing. He began to arrange other composers' music, including a set of 53 exceptional etudes on Chopin's etudes, as well as other music. While teaching in Chicago, he gained a strong local reputation by giving recitals. An eight-recital set in 1897 and 1898 surveyed the history of nineteenth century piano literature.
Soon his fame spread, and he had triumphal performances in the U.S. and Europe. His December 6, 1900, concert at Beethoven Hall in Berlin was a triumph where he was acclaimed one of the greatest living pianists. Soon, he was the highest-paid solo instrumentalist in the world. He continued to write original piano music and his free adaptations of other music. In 1909, he became director of the Piano School of the Imperial Academy of Music in Vienna, the first Jew to take this post.
He was visiting Belgium for vacation in 1914 when the Germans invaded. He escaped to England and returned to the United States, where he made his home for the rest of his life. He moved his residence frequently and traveled widely, giving concerts in Mexico, South America, Yokohama, and Asia. His trip to Java inspired him to try to capture the sound of the gamelan orchestra in his suite Phonoramas. He lost much of his fortune in the 1929 stock market crash, then the next year had a severe stroke that ended his public career. He declined into depression and further illness before his death.