There is growing evidence that climatic factors could influence the evolution of the current COVID-19 pandemic. Here, we build on this evidence base, focusing on the southern hemisphere summer and autumn period. The relationship between climatic factors and COVID-19 cases in New South Wales, Australia was investigated during both the exponential and declining phases of the epidemic in 2020, and in different regions. Increased relative humidity was associated with decreased cases in both epidemic phases, and a consistent negative relationship was found between relative humidity and cases. Overall, a decrease in relative humidity of 1% was associated with an increase in cases of 7-8%. Overall, we found no relationship with between cases and temperature, rainfall or wind speed. Information generated in this study confirms humidity as a driver of SARS-CoV-2 transmission.