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Marine heatwaves (MHWs) pose an increasing threat to the ocean's wellbeing as global warming progresses. Forecasting MHWs is challenging due to the various factors that affect their occurrence, including large variability in the atmospheric state. In this study we demonstrate a causal link between ocean heat content and the area and intensity of MHWs in the Tasman Sea on interannual to decadal time scales. Ocean heat content variations are more persistent than 'weather-related' atmospheric drivers (e.g., blocking high pressure systems) for MHWs and thus provide better predictive skill on timescales longer than weeks. Using data from a forced global ocean sea-ice model, we show that ocean heat content fluctuations in the Tasman Sea are predominantly controlled by oceanic meridional heat transport from the subtropics, which in turn is mainly characterized by the interplay of the East Australian Current and the Tasman Front. Variability in these currents is impacted by wind stress curl anomalies north of this region, following Sverdrup's and Godfrey's 'Island Rule' theories. Data from models and observations show that periods with positive upper (2000 m) ocean heat content anomalies or rapid increases in ocean heat content are characterized by more frequent, larger, longer and more intense MHWs on interannual to decadal timescales. Thus, the oceanic heat content in the Tasman Sea acts as a preconditioner and has a prolonged predictive skill compared to the atmospheric state (e.g., surface heat fluxes), making ocean heat content a useful indicator and measure of the likelihood of MHWs.