Actuator faults in wind turbines (WT) significantly increase the structural loads exhibited by torsional vibration and tower fore-aft bending, thereby, drastically hampering the turbine health in terms of the reduction in its lifetime. This paper presents a health-aware fault-tolerant control (HAFTC) scheme for WT such that the turbine health, i.e., power maximization and fatigue reduction, can be achieved even under the event of bias faults in converter actuator. The proposed HAFTC system is built upon two interconnected modules: fault diagnosis and controller reconfiguration. The latter module is developed using a receding horizon control technique where the underlying optimization problem is not convex. The originality of the proposed scheme lies in the transformation of the initial non-convex optimization problem into a convex problem. The former module extracts the complete information of the fault, which is constructed using an unknown-input-observer based residual filter and a specific fault-estimation filter. A 2MW WT system is used to demonstrate the effectiveness of the HAFTC scheme.