Using the backstepping design, we achieve exponential stabilization of the coupled Saint-Venant-Exner (SVE) PDE model of water dynamics in a sediment-filled canal with arbitrary values of canal bottom slope, friction, porosity, and water-sediment interaction under subcritical or supercritical flow regime. This model consists of two rightward and one leftward convecting transport Partial Differential Equations (PDEs). A single boundary input control (with actuation located only at downstream) strategy is employed and the backstepping approach developed for the first order linear hyperbolic PDEs is used. A full state feedback controller is designed, which guarantees the exponential stability of the closed-loop control system.