A recently developed method for scaling Richards’ equation during soil-water redistribution was extended here to derive invariant solutions for solute transport for a range of soils and initial conditions. Any arbitrary model for hydraulic properties can be used in Richards’ equation. A transport model including both terms of convection and diffusion/dispersion is considered where the soil–solute reactions described by a linear sorption isotherm are considered. To evaluate the proposed method, Hydrus-1D simulations were used to solve the water flow and solute transport equations for various soil textures and initial conditions. The resulting soil water content and solute concentrations profiles were scaled using the proposed method. The scaled results were nearly invariant for loam to clay soil textures and for a variety of initial conditions. The invariance of the scaled results implies a robust approach to scaling water flow and solute transport during the redistribution process and readily produces approximate solutions of the highly nonlinear governing equations.