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Abstract Understanding drivers of river mobility—temporal shifts in river channel positions—is critical for managing fluvial landscapes sustainably and for interpreting past river responses to climate change. However, direct observations linking river mobility and water discharge variability are scarce. Here, we pair multi‐annual measurements of daily water discharge and river mobility, estimated from Landsat, for 48 rivers worldwide. We show that, across climates and planforms, river mobility is correlated with water discharge variability over daily, intra‐annual, and inter‐annual timescales. For similar mean discharge, higher discharge variability is associated with up to an order‐of‐magnitude faster floodplain reworking. A random forest regression model indicates that discharge variability is the primary predictor of river mobility, when compared to mean water discharge, sediment concentration, and channel‐bed slope. Our results suggest that enhanced hydro‐climatic extremes could accelerate future river mobility, and that past changes to discharge variability may explain the fabric of fluvial strata.