Godowsky was born in Soshly, near Vilnius, in what is now Lithuania. As a child, he received some lessons in basic piano playing and music theory; at age fourteen, he entered the Königliche Hochschule für Musik in Berlin, where he studied under Ernst Rudorff, but left after three months. Otherwise, he was self-taught.
His career as a concert pianist, which eventually would take him to every continent except Australia and Antarctica, began at age ten. In 1886, after a tour of North America, he returned to Europe, intending to study with Franz Liszt in Weimar. Upon learning of Liszt's death shortly after his return, he traveled instead to Paris, where he was befriended by the composer and pianist Camille Saint-SaŽns, who enabled him to make the acquaintance of many leading French musicians. Saint-SaŽns even proposed to adopt Godowsky if he would take his surname, an offer which Godowsky declined, much to the older man's displeasure.
Godowsky's pedagogical activity began in 1890 at the New York College of Music. While in New York, he married Frieda Saxe and became an American citizen. In 1894 he moved to the Broad Street Conservatory in Philadelphia, and again in 1895 to the Chicago Conservatory, where he headed the piano department. A successful European concert tour in 1900 landed him once again in Berlin, where he divided his time between performing and teaching. From 1909 to 1914 he taught master classes at the Vienna Academy of Music. The outbreak of World War I drove him back to New York, where his home was frequented by many distinguished performers and celebrities of that day. Sergei Rachmaninov, a particular friend, dedicated his Polka de W. R. to him.
After the war, Godowsky resumed touring, but a stroke he suffered June 17, 1930, during a recording session in London, put an end to his public performances, and made it impossible for him to recoup the considerable financial loss he had suffered in the Wall Street Crash of 1929. The suicide of his younger son in 1932 and the death of his wife in 1933, combined with his despair over the deteriorating political situation in Europe (his plans for a "World Synod of Music and Musicians" and an "International Master Institute of Music" came to nothing) cast an even deeper shadow over his last years, and he stopped composing. He died of stomach cancer in New York on November 21, 1938.
As a composer, Godowsky is best known for his paraphrases of piano pieces by other composers, which he enhanced with ingenious contrapuntal devices and rich chromatic harmonies. His most famous work in this genre is the 53 Studies on Chopin's Etudes, in which he varies each of the already challenging originals by introducing countermelodies, transferring the technically difficult passages from the right hand to the left, or by transcribing the entire etude for left hand solo. These are so taxing even for virtuosi that as of today (2004) only three have ventured to record the entire set: Geoffrey Douglas Madge, Carlo Grante, and Marc-André Hamelin.