This work demonstrates a general method for simulating multicomponent diffusion in concentrated solutions using molecular dynamics (MD). Although there have been prior reports of MD simulations of diffusion in multicomponent systems, no fully rigorous expressions have been reported for simulating Stefan-Maxwell diffusivities for an arbitrary number of species. The Green-Kubo approach developed here allows for the computation of a full diffusion-coefficient matrix for any number of species. The development is applicable to any solution that can be simulated using MD; nevertheless, our primary interest is in electrochemical applications. To this end, the method is tested by simulations of aqueous KCl and NaCl salt solutions in the concentration range 1-4 m. Intermolecular potentials were parametrized for these transport-based simulations. This work is the first to simulate all three independent diffusion coefficients for these solutions. The results are in semi quantitative agreement with experiment and show that Green-Kubo calculations are realizable for concentrated electrolytes and other solutions.