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Knowledge of drought onset and its relationship with drought severity (deficit volume) is crucial for providing timely information for reservoir operations, irrigation scheduling, devising cropping choices and patterns and managing surface and groundwater water resources. An analysis of the relationship between drought onset timing and deficit volume can help in drought hazard assessments and associated risks. Despite its importance, little attention has been paid to understand the drought onset timing and its potential linkage with deficit volume for effective drought monitoring and its impact assessment. Further, only a few studies have explored the role of environmental controls, encompassing the interaction between climate, catchment and land‐surface processes in influencing streamflow droughts and associated characteristics such as onset time and severity. This study leverages quality‐controlled streamflow observations from 1965 to 2018 to unveil regional patterns of streamflow drought onset, at‐site trends in deficit volume and detect non‐linear relationships between onset timing and deficit volume across 82 rain‐fed catchments in peninsular India (8°–24° N, 72°–87° E). We show that around 12% of catchments show an earlier onset of streamflow droughts in conjunction with a decreasing trend in deficit volume. Further, approximately one‐third of the catchments show a significant non‐linear dependency between drought deficit volume and onset time. Among catchment controls, such as soil and topographic properties, we found soil organic carbon stock and stock as dominant drivers controlling the streamflow drought onset time. Likewise, sand content and vertical distance to channel network control the streamflow deficit volume. Finally, the linkages between inferred dominant low‐flow generation mechanisms and the specific combinations of environmental controls are synthesized in a conceptual diagram that might assist in developing appropriate models for low‐flow simulations and predictions, especially across ungauged sites. The new insights add value to understanding the chain of physical processes linking climatic and physiographic controls on streamflow droughts, which can support drought forecasting and climate impact assessment efforts. [ABSTRACT FROM AUTHOR]