A new Anti-Windup Bumpless Transfer (AWBT) scheme for state constrained linear systems is presented. The AWBT strategy is based on the design of a special limiting circuit in the framework of standard AWBT control. The limiting circuit involves a two step calculation: first, the effect of the current control action over future state constraints is predicted; next, if any violation of the constraints is detected, an allowed control action is back-calculated. The resulting control action is such that the offending constrained states are taken to their saturation limits. Connections between the proposed state constraint AWBT scheme and Model Predictive Control (MPC) are also investigated. The state constraint AWBT and MPC strategies are shown to be equivalent in a non-trivial region of the state space.