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• Estimates of the time of emergence of climate change (ToE) for Australian rivers. • Stochastic data generation helps to better define baseline variability. • Uncertainty in ToE represented by 37 CMIP6 projections and 3 emissions scenarios. • ToE in river flows can precede ToE in precipitation by up to 50 years. • ToE substantially delayed or avoided in a low emissions pathway (SSP1-2.6). Climate change impacts on river flows are leading to substantial changes in water availability for human and natural systems. The significance of these impacts largely depends on the degree of change relative to natural variability. The 'Time of Emergence' (ToE) is the point in time (past or future) when the signal of climate change emerges from the noise of background variability. The ToE has been assessed for some climate variables but rarely streamflows. Here we investigate ToE of changes in streamflow across Australia for various characteristic periods relevant to different water management objectives. We assess the uncertainty in ToE estimates from different emissions pathways and a large ensemble of CMIP6 climate model projections. ToE is likely to occur earlier in hydrologic systems subject to low natural variability than those subject to high variability, and to systems that are vulnerable to failure over longer rather than shorter periods. There are clear regional differences in the patterns of ToE, with changes first emerging in south-west regions of Australia, followed by the south-east, then east and north. We estimate that ToE has already occurred in over 10% of sampled rivers for longer characteristic periods, primarily in south-west Australia. Importantly for planning, the results show that ToE in flows precedes ToE in precipitation by up to 50 years due to compounding effects of changes in annual precipitation, precipitation seasonality, and increasing temperatures. The number of catchments projected to have reached ToE by 2080 is heavily influenced by the trajectory of future emissions. A low emissions pathway generally consistent with aspirational goals of the Paris Climate Agreement (SSP1-2.6) substantially delays the emergence of significant hydrological change by up to 50 years, or negates emergence entirely by 2080, depending on location. Our methods can be applied to catchments globally, and our findings have implications for the prioritisation of climate adaptation efforts across different river systems and the urgency of continued action on climate change mitigation. [ABSTRACT FROM AUTHOR]