Since 1995, a large region of Australia has been gripped by the most severe drought in living memory, the so-called “Big Dry”. The ramifications for affected regions are dire, with acute water shortages for rural and metropolitan areas, record agricultural losses, the drying-out of two of Australia's major river systems and far-reaching ecosystem damage. Yet the drought's origins have remained elusive. For Southeast Australia, we show here that the “Big Dry” and other iconic 20th Century droughts, including the Federation Drought (1895–1902) and World War II drought (1937–1945), are driven by Indian Ocean variability, not Pacific Ocean conditions as traditionally assumed. Specifically, a conspicuous absence of Indian Ocean temperature conditions conducive to enhanced tropical moisture transport has deprived southeastern Australia of its normal rainfall quota. In the case of the “Big Dry”, its unprecedented intensity is also related to recent higher temperatures.