Chronic exposure to arsenic (As) via drinking groundwater is a human health concern worldwide. Probabilities of elevated geogenic As concentrations in groundwater were predicted in complex, glacial aquifers in Minnesota, north‐central USA, a region that commonly has elevated As concentrations in well water. Maps of elevated As hazard were created for depths typical of drinking water supply and with well construction attributes common for domestic wells. Conventional variables describing aquifer properties and materials, position on the hydrologic landscape, and soil geochemistry were among the most influential for predicting the probability of elevated As. We also found that certain well construction attributes were influential in predicting As hazard. Smaller distances between the top of the well screen and overlying aquitard (proximity) and shorter well screen lengths were each associated with higher probabilities of elevated As. Influential predictor variables, which are either mapped across the region or are well construction attributes, are proxies in the model for measurable physical or geochemical causes of elevated As (e.g., redox condition, till or aquifer sediment chemistry, and water chemistry), which are not mapped across the region. Our setting shares some important characteristics with deltaic and other high‐As aquifers in Southeast Asia: late Quaternary age, complex layering of coarse‐ and fine‐grained materials, low‐As sediment concentrations, and geochemical controls on As mobilization. Translating three‐dimensional geologic and geochemical understanding of As mobility to quantifiable variables for modeling with powerful, flexible statistical tools could improve predictions and help identify safer groundwater supply options in the USA, Southeast Asia, and elsewhere.