Extreme rainfall conditions in Australia during the 2010/2011 La Niña resulted in devastating floods claiming 35 lives, causing billions of dollars in damages, and far-reaching impacts on global climate, including a significant drop in global sea level and record terrestrial carbon uptake. Northeast Australian 2010/2011 rainfall was 84% above average, unusual even for a strong La Niña, and soil moisture conditions were unprecedented since 1950. Here we demonstrate that the warmer background state increased the likelihood of the extreme rainfall response. Using atmospheric general circulation model experiments with 2010/2011 ocean conditions with and without long-term warming, we identify the mechanisms that increase the likelihood of extreme rainfall: additional ocean warming enhanced onshore moisture transport onto Australia and ascent and precipitation over the northeast. Our results highlight the role of long-term ocean warming for modifying rain-producing atmospheric circulation conditions, increasing the likelihood of extreme precipitation for Australia during future La Niña events.