A two-degree-of-freedom LQGPC optimal control law is derived, which has properties in common with both the LQG and GPC control laws. The stability and robustness properties are the same as for an LQG optimal controller, but the cost of future predictive error and control action is dealt with in the same manner as for the GPC control law. An advantage of the approach is that true predictive action is possible, so the control at time t will optimally use the future reference-trajectory knowledge. The feedback controller to be implemented is time-invariant, but the future predicted control action is obtained from the polynomial equivalent of a time-varying solution, which is analogous to the solution of the finite-time deterministic LQ optimal control problem. The results can be presented in a form similar to that employed in GPC algorithms, suggesting an immediate way of achieving input and output constraints.