The mechanisms leading to megafauna (>44 kg) extinctions in Late Pleistocene (126,000-12,000 years ago) Australia are highly contested because standard chronological analyses rely on scarce data of varying quality and ignore spatial complexity. Relevant archaeological and palaeontological records are most often also biased by differential preservation resulting in under-representated older events. Chronological analyses have attributed megafaunal extinctions to climate change, humans, or a combination of the two, but rarely consider spatial variation in extinction patterns, initial human appearance trajectories, and palaeoclimate change together. Here we develop a statistical approach to infer spatio-temporal trajectories of megafauna extirpations (local extinctions) and initial human appearance in south-eastern Australia. We identify a combined climate-human effect on regional extirpation patterns suggesting that small, mobile Aboriginal populations potentially needed access to drinkable water to survive arid ecosystems, but were simultaneously constrained by climate-dependent net landscape primary productivity. Thus, the co-drivers of megafauna extirpations were themselves constrained by the spatial distribution of climate-dependent water sources.