Although it is traditionally thought that drainage basins are geometrically similar, we present new results which indicate that the aspect ratio of weakly dissected river basins at large scales (10–103 km2) depends on the surface slope: steeper surfaces develop narrower and lengthier basins whereas more gently dipping surfaces develop more equant and wider basins. This relationship is interpreted to be related to the nature of water flow over rough surfaces, with steeper slopes causing less flow convergence and lengthier and narrower basins. We derive an empirical relationship that can be used to infer the slope of a surface on which a river basin acquired its geometry based solely on a measure of its basin form. This relation provides a unique means of inferring the relative chronology of river basin development with respect to surface tilting and therefore provides a direct link between river basin morphology and tectonics.