After studying privately in Santiago for two years, Arrau went to Berlin, where he studied with Martin Krause, a pupil of Franz Liszt, from 1912 to 1918. His serious career began with a recital in Berlin in 1914, and during the next decade he toured extensively in Europe, South America, and the United States. Between 1924 and 1940 he taught at Julius Stern's Conservatory in Berlin, and in 1941 he moved permanently to the United States. He continued his frequent touring past his 80th birthday.

Arrau concentrated on the music of Liszt, Johannes Brahms, Frédéric Chopin, Robert Schumann, Claude Debussy, and, above all, Ludwig van Beethoven. Regarded as one of the least ostentatious of the virtuoso pianists, Arrau developed a classical approach that exhibited an extreme concentration on detail, without sacrificing feeling.