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Recent marine heatwave (MHW) events in the Tasman Sea have had dramatic impacts on the ecosystems, fisheries, and aquaculture off Tasmania's east coast. However, our understanding of the large-scale drivers (forcing) and potential predictability of MHW events in this region off southeast Australia is still in its infancy. Here, we investigate the role of oceanic Rossby waves forced in the interior South Pacific on observed MHW occurrences off southeast Australia from 1994 to 2016, including the extreme 2015/16 MHW event. First, we used an upper-ocean heat budget analysis to show that 51% of these historical Tasman Sea MHWs were primarily due to increased East Australian Current (EAC) Extension poleward transports through the region. Second, we used lagged correlation analysis to empirically connect the EAC Extension intensification to incoming westward-propagating sea surface height (SSH) anomalies from the interior South Pacific. Third, we dynamically analyzed these SSH anomalies using simple process-based baroclinic and barotropic Rossby wave models forced by wind stress curl changes across the South Pacific. Finally, we show that associated monthly SSH changes around New Zealand may be a useful index of western Tasman Sea MHW predictability, with a lead time of 2–3 years. In conclusion, our findings demonstrate that there is potential predictability of advection-dominated MHW event likelihoods in the EAC Extension region up to several years in advance, due to the deterministic contribution from baroclinic and barotropic Rossby waves in modulating the EAC Extension transports. [ABSTRACT FROM AUTHOR]