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Abstract We present a novel quantitative test of a 50‐year‐old hypothesis which asserts that river delta morphology is determined by the balance between river and marine influence. We define three metrics to capture the first‐order morphology of deltas (shoreline roughness, number of distributary channel mouths, and presence/absence of spits), and use a recently developed sediment flux framework to quantify the river‐marine influence. Through analysis of simulated and field deltas we quantitatively demonstrate the relationship between sediment flux balance and delta morphology and show that the flux balance accounts for at least 35% of the variance in the number of distributary channel mouths and 42% of the variance in the shoreline roughness for real‐world and simulated deltas. We identify a tipping point in the flux balance where wave influence halts distributary channel formation and show how this explains morphological transitions in real world deltas.