A method to determine the soil hydraulic conductivity via an internal drainage experiment is presented. Identifying the parameters of the hydraulic conductivity is achieved by solving an inverse global optimization problem that uses the water contents measured at different depths and times as matching flow variables. The optimization procedure is combined with a recently developed analytical model for the water content propagation, which essentially assumes that the flow is gravity-driven. A crucial (from the identification point of view) parameter of such a model is the initial position zW of the draining front, determining the interface between the wetted and dried zone. By using an evolutionary algorithm specifically developed for this problem, it is shown that if information upon zW is not a priori available, the identification of the hydraulic conductivity is not possible. However, assuming that zW is known (i.e. measured), and by dividing the model variables by zW, the optimization is able to fully identify the soil hydraulic conductivity. Finally, in order to show the robustness of the proposed approach, it is shown that the method leads to very good estimates of the hydraulic conductivity even if data are noise-affected, provided that the optimization procedure is coupled to the (Tikhonov) regularization approach.