We show that drainage basin morphology correlates with climate. Computational analysis of the 46 basins extracted from the western slopes of the Andes reveals the existence of four different basin morphologic classes. This purely geomorphic partition correlates with division of the same basins on the grounds of climate types. Basins are compared using circularity functions as their formal representations. Self-organizing maps and dendrograms are employed to provide basin classification. One class of basin morphologies corresponds to sites in the arid Atacama Desert, and the other class corresponds to sites in the Atacama exhibiting groundwater sapping landforms. Using the same technique, we study a larger sample of 94 basins that, in addition to the Andean basins, includes other terrestrial basins and 26 basins from Martian sites that show prominent valley networks. The classification of this larger set shows that morphologies of Martian and terrestrial basins bifurcate at the root of the dendrogram, forming two separate domains of basin morphologies. The similarity map reveals that, of all the terrestrial basins, the Atacama Desert basins are morphologically closest to the Martian basins. Extrapolating the terrestrial morphology-climate linkage to Mars points to formation of valley networks in a hyperarid climatic environment. We submit that the Atacama Desert provides the best possible terrestrial morphologic analog to valley network sites on Mars. We discuss climatic and hydrologic particularities of the Atacama Desert and hypothesize that a similar environment existed on early Mars.