Based on model output from a multi-model ensemble (MME) of coupled atmosphere-ocean general circulation models, it is shown that prolonged trends in Australian rainfall over the southwest during winter and the monsoonal northwest during summer are associated with trends in the large scale Southern Hemisphere circulation. These trends, in turn, are the result of external radiative forcing, including anthropogenic greenhouse gases, ozone, aerosols and land use change. The MME is used in an analysis of covariance method to separate the internal (natural) variability in the coupled rainfall-atmospheric circulation relationship from influences associated with anomalous external radiative forcing. In both seasons, the leading coupled external mode (singular vector) in the twentieth century runs has rainfall and circulation loading patterns with associated time-series that have statistically significant trends. The associated rainfall loading patterns qualitatively resemble the patterns of observed rainfall trends. The circulation loading patterns reflect the thermal expansion of the tropics and the Hadley Cell. A comparison between similar analyses using the second half of the twenty-first century of the representative concentration pathways (RCP) RCP8.5 and RCP4.5 scenarios show that trends in rainfall and the circulation are projected to continue and intensify under increasing anthropogenic greenhouse gas concentrations. The technique developed here is generally applicable to separate the climate change signal from natural variability in any relevant pair of coupled climate fields.