This paper addresses predictive state regulation of linear discrete-time systems subject to persistent bounded disturbances and to state and/or control constraints. It is well known that the joint presence of constraints and disturbances can drive a predictive controller to infeasibility and instability. Here it is shown how robustness against persistent bounded disturbances can be enforced by inserting in the predictive controller suitable constraint restrictions. The robust predictive controller obtained in this way guarantees, for all admissible disturbances, constraint fulfillment and asymptotic state regulation, i.e. convergence of the state to a minimal robust invariant set, provided that the initial state is feasible. Simulation results demonstrate the effectiveness of the proposed approach.