Traffic control measures like variable speed limits or outflow control can be used to influence the route choice of drivers. In this paper we develop a day-to-day route choice control method that is based on model predictive control (MPC). A basic route choice model forms the basis for the controller. We show that for the given model and for a linear cost function it is possible to reformulate the MPC optimization problem as a mixed-integer linear programming (MILP) problem. For MILP problems efficient branch-and-bound solvers are available that guarantee to find the global optimum. We also illustrate the efficiency of the proposed approach for a simple simulation example involving speed limit control.