This paper proposes an optimal active power dispatch algorithm for wind farms based on wind turbine (WT) load sensitivity. The control objectives include tracking power references from the system operator and minimizing fatigue loads experienced by WTs. The sensitivity of WT fatigue loads to power references is defined which simplifies the formulation of the optimal power dispatch problem. Since the sensitivity value is calculated at the local WT controller, the computation burden of the central wind farm controller is largely reduced. Moreover, explicit analytical equations of the fatigue load sensitivity are derived, which significantly improves the computation efficiency of the local WT controller. The proposed algorithm can be implemented in different active power control schemes. Case studies were conducted with a wind farm under balance control for both low and high wind conditions. By comparing the rainflow cycles and damage equivalent load (DEL), the efficacy of the proposed algorithm is verified.