Predicting solute transport through structured soil based on observable structural properties of the material has not been accomplished to date. We evaluated a new approach to predicting breakthrough curves (BTCs) of dissolved chemicals in intact structured soil columns based on attributes of the pore structure at hierarchical spatial scales. The methodology centers on x-ray computed microtomography of a hierarchic suite of undisturbed soil samples (diameters 1, 4.6, 7.5, and 16 cm) to identify the network of pores >10 μm in diameter. The pore structure was quantified in terms of pore size distribution, interface area density, and connectivity. The pore size distribution and pore connectivity were used to set up an equivalent pore network model (PNM) for predicting the BTCs of Br− and Brilliant Blue FCF (BB) at unsaturated, steady-state flux. For a structured silt loam soil column, the predictions of Br− tracer breakthrough were within the variation observed in the column experiments. A similarly good prediction was obtained for Br− breakthrough in a sandy soil column. The BB breakthrough observed in the silt loam was dominated by a large variation in sorption (retardation factors between R = 2.9 and 24.2). The BB sorption distribution coefficient, kd, was measured in batch tests. Using the average kd in the PNM resulted in an overestimated retardation (R = 28). By contrast, breakthrough of BB in the sandy soil (experimental R = 3.3) could be roughly predicted using the batch test kd (PNM simulation R = 5.3). The prediction improved when applying a sorption correction function accounting for the deviation between measured interface area density distribution and its realization in the network model (R = 4.1). Overall, the results support the hypothesis that solute transport can be estimated based on a limited number of characteristics describing pore structure: the pore size distribution, pore topology, and pore–solid interfacial density.