The southwest corner of Western Australia has been subject to a serious drought in recent decades. A range of factors, such as natural variability and changes in land use, ocean temperatures and atmospheric circulation, have been implicated in this drought, but the ultimate cause and the relative importance of the various factors remain unclear. Here we report a significant inverse correlation between the records of precipitation at Law Dome, East Antarctica and southwest Western Australia over the instrumental period, including the most recent decades. This relationship accounts for up to 40% of the variability on interannual to decadal timescales, and seems to be driven by the meridional circulation south of Australia that simultaneously produces a northward flow of relatively cool, dry air to southwest Western Australia and a southward flow of warm, moist air to East Antarctica. This pattern of meridional flow is consistent with some projections of circulation changes arising from anthropogenic climate change. The precipitation anomaly of the past few decades in Law Dome is the largest in 750 years, and lies outside the range of variability for the record as a whole, suggesting that the drought in Western Australia may be similarly unusual.