Sensor-based optimal spacecraft attitude reorientation control by momentum exchange based on a computational programming approach is addressed in this study. The control problem of a rigid spacecraft actuated by more than three reaction wheels with an open time of maneuver is considered. The modified Rodrigues parameters for large principal rotations are applied to derive our kinematical model. The introduced algorithm can be realized by attitude sensors, such as rate gyros, with an appropriate arrangement. The cost function to be minimized is defined as a weighted performance index of the time of the maneuver and the integral of the squared sum of wheel-torque magnitudes. Instead of utilizing Pontryagin’s minimum principle, an iterative procedure is used to reformulate and solve the optimal reorientation control problem as a constrained nonlinear programming problem. To show the feasibility of the proposed method, numerical simulated results are included for illustration.