Basin‐scale models are required to interpret ancient continental sedimentary successions, and reduce uncertainty in assessing geological resources in basins. Recently, modern studies show distributive fluvial systems to comprise a substantial proportion of modern sedimentary basins, but their role in ancient basin fills has yet to be quantitatively documented at the basin scale. This study analysed key fluvial characteristics to construct a detailed basin‐wide model of the Palaeogene Fort Union and Willwood formations (Bighorn Basin, Wyoming), using observations from modern studies, and ancient system scale studies of distributive fluvial systems, to guide interpretations. Mapping showed these formations to be highly heterogeneous with channel‐body proportion (from 12 to 81%) and geometry types (large amalgamated bodies to isolated channels), grain size (silt to conglomerate), average channel‐body thickness (4 to 20 m) and average storey thickness (3 to 10 m) varying significantly across the basin. Distributive fluvial systems in the form of alluvial and fluvial fans in transverse configurations were recognized as well as a wide axial system, with heterogeneity in the formations being closely aligned to these interpretations. Furthermore, numerous individual depositional systems were identified within the formations (Beartooth Absaroka, Washakie, Owl Creek and axial). Predicted downstream distributive fluvial system trends (i.e. downstream decrease in channel proportion, size and grain size) were identified in the Beartooth, Absaroka and Owl Creek systems. However, predicted trends were not identified in the Washakie system where intrabasinal thrusting disturbed the sequence. Importantly, a wide axial fluvial system was identified, where reverse downstream distributive fluvial system trends were present, interpreted to be the result of the input of transverse systems of variable size. This study provides a new level of detail in the application of basin‐scale models, demonstrating their usefulness in trying to understand and predict alluvial architecture distribution and heterogeneity, with important implications for economic resources and palaeogeographic reconstructions.