Gaussian setting time is the time scale at which solute plumes converge to their asymptotic Gaussian shape. This study estimates the Gaussian setting time using a high‐resolution hydrofacies model of a typical fluvial system, with an instantaneous point source in the mobile phase. Monte Carlo simulations are augmented by a time‐nonlocal transport model to forecast plume shape at late time. Analysis of plume spatial moments indicates that convergence to Fickian transport is affected by molecular diffusion and the thickness of low‐permeability floodplain layers. These layers can cause non‐Gaussian tailing to persist at late time because the low‐permeability lenses are elongated in the horizontal, so that most particles escape vertically by diffusion. A simple empirical setting time formula is developed, which can be fitted using data from driller's logs that characterize the thickness of the low‐permeability lenses. The empirical formula may be useful for predicting setting time in fluvial aquifers similar to those considered in this study. For such aquifers, the plume will often exit the region prior to the setting time, so the asymptotic Gaussian model will not be a useful predictor of plume shape.