The discovery of remarkably rounded pebbles by the rover Curiosity, within an exhumed alluvial fan complex in Gale Crater, presents some of the most compelling evidence yet for sustained fluvial activity on Mars. While rounding is known to result from abrasion by inter-particle collisions, geologic interpretations of sediment shape have been qualitative. Here we show how quantitative information on the transport distance of river pebbles can be extracted from their shape alone, using a combination of theory, laboratory experiments and terrestrial field data. We determine that the Martian basalt pebbles have been carried tens of kilometres from their source, by bed-load transport on an alluvial fan. In contrast, angular clasts strewn about the surface of the Curiosity traverse are indicative of later emplacement by rock fragmentation processes. The proposed method for decoding transport history from particle shape provides a new tool for terrestrial and planetary sedimentology.