While it is established that low-frequency climate variability modes have a dominant role on Australia's climate, limited work to date has focused on relationships between climate variability and Australian heatwaves. Moreover, heatwaves are a distinctive type of extreme weather that can be classified by multiple characteristics, such as intensity, frequency, duration, and timing. This study identifies the relationships between known modes of climate variability that influence Australian climate, and discrete seasonal characteristics of the intensity, frequency, duration, and timing of heatwaves. The large-scale seasonal modes of the El Niño/Southern Oscillation (ENSO), the Indian Ocean Dipole (IOD), and the Southern Annular Mode (SAM) are investigated for extended Austral summers commencing between the years 1911 and 2012. While ENSO is found to have the strongest relationship with Australian heatwave characteristics, this study finds that ENSO's influence differs between heatwave frequency, duration, intensity, and timing. Regions dominated by ENSO experience more, longer lasting and hotter heatwaves combined with an earlier commencement of the heatwave season during El Niño phases. The exception to this is southeast Australia, where SAM is generally more dominant. In contrast, the IOD provides little indication of seasonal heatwave characteristics due to its relative inactivity during the Austral summer months. Lastly, we show that antecedent soil moisture has varying strengths of relationships with Australian heatwave characteristics, exhibiting relationships with heatwave intensity and timing over some regions where none are detected between large-scale modes. However, while significant relationships between dry antecedent soil moisture and extreme heatwaves do exist over Australia, these appear to be slightly weaker than similar relationships over Europe reported in other studies.