In deserts, the interplay between occasional fluvial events and persistent aeolian erosion can form composite modern and relict surfaces, especially on the distal portion of alluvial fans. There, relief inversion of alluvial deposits by differential erosion can form longitudinal ridges. We identified two distinct ridge types formed by relief inversion on converging alluvial fans in the hyperarid Chilean Atacama Desert. Although they are co-located and similar in scale, the ridge types have different ages and formation histories that apparently correspond to minor paleoclimate variations. Gravel-armored ridges are remnants of deflated alluvial deposits with a bimodal sediment distribution (gravel and sand) dated to a minor pluvial phase at the end of the Late Pleistocene (~12 kyr). In contrast, younger (~9 kyr) sulfate-capped ridges formed during a minor arid phase with evaporite deposition in a pre-existing channel that armored the underlying deposits. Collectively, inverted channels at Salar de Llamara resulted from multiple episodes of surface overland flow and standing water spanning several thousand years. Based on ridge relief and age, the minimum long-term deflation rate is 0.1–0.2 m/kyr, driven primarily by wind erosion. This case study is an example of the equifinality concept whereby different processes lead to similar landforms. The complex history of the two ridge types can only be generally constrained in remotely sensed data. In situ observations are required to discern the specifics of the aqueous history, including the flow type, magnitude, sequence, and paleoenvironment. These findings have relevance for interpreting similar landforms on Mars.