Wind power intermittency represents one of the major challenges facing the future growth of grid-connected wind energy projects. The integration of wind turbines and energy storage systems (ESS) provides a viable approach to mitigate the unfavorable impact on grid stability and power quality. In this study, an economic model predictive control (MPC) framework is presented for an integrated wind turbine and flywheel energy storage system (FESS). The control objective is to smooth wind power output and mitigate tower fatigue load. The optimal control problem within the model predictive control framework has been formulated as a convex optimal control problem with linear dynamics and convex constraints that can be solved globally. The performance of the proposed control algorithm is compared to that of a baseline wind turbine controller. The effect of the proposed control actions on the fatigue loads acting on the tower and blades is investigated. The simulation results, with various wind scenarios, showed the ability of the proposed control algorithm to achieve the aforementioned objectives in terms of smoothing output power and mitigating tower fatigue load with negligible effect on the wind energy harvested.