This paper introduces motion control scheme of a new aerial manipulation system that consists of 2-link manipulator attached to the bottom of a quadrotor. This new system presents a solution for the limitations found in the current quadrotor manipulation systems. It is very attractive for a wide range of applications due to their unique features. However, control of such system is quite challenging because it is naturally unstable, has strong nonlinearities and couplings, has fast dynamics, is very susceptible to parameters variations due to carrying a payload besides the external disturbances like wind, and has actuator limitations. A robust optimal linear control scheme is proposed to address these issues. The proposed control scheme is based on a hybrid linear Model Predictive Control (MPC) and linear Disturbance Observer (DOb) techniques. The motivation for using DOb is to provide the robustness against the nonlinearities/uncertainties. In addition, it allows one to solve the control problem relying on a set of linear decoupled SISO system which are not affected by nonlinear/uncertain terms. To deal with the actuators' constraints and achieve an optimal controller efforts, a standard MPC will be used. The resulting control scheme is characterized by a low computational load with respect to conventional nonlinear robust solutions. Stability analysis of the proposed control system is presented. The controller is tested to achieve of a point-to-point task space control, under the effect of picking/placing a payload, changing the operating region, and measurement noise. System simulation is implemented in MATLAB/SIMULINK environment with real system parameters, to better emulate a realistic set up. Simulation results enlighten the effectiveness of the proposed control technique.