Hybrid aircraft configurations with combined cruise and vertical flight capabilities are increasingly being considered for unmanned aircraft and urban air mobility missions. To ensure the safety and autonomy of such missions, control challenges including fault tolerance and windy conditions must be addressed. This paper presents an observer-based optimal control approach for the active combined fault and wind disturbance rejection, with application to a quadplane unmanned aerial vehicle. The quadplane model is linearised for the longitudinal plane, vertical takeoff and landing and transition modes. Wind gusts are modelled using a Dryden turbulence model. An unknown input observer is first developed for the estimation of wind disturbance by defining an auxiliary variable that emulates body referenced accelerations. The approach is then extended to simultaneous rejection of intermittent elevator faults and wind disturbance velocities. Estimation error is mathematically proven to converge to zero, assuming a piecewise constant disturbance. A numerical simulation analysis demonstrates that for a typical quadplane flight profile at 100 m altitude, the observer-based wind gust and fault correction significantly enhances trajectory tracking accuracy compared to a linear quadratic regulator and to a H-infinity controller, which are both taken, without loss of generality, as benchmark controllers to be enhanced. This is done by adding wind and fault compensation terms to the controller with admissible control effort. The proposed observer is also shown to enhance accuracy and observer-based rejection of disturbances and faults compared to three alternative observers, based on output error integration, acceleration feedback and a sliding mode observer, respectively. The proposed approach is particularly efficient for the active rejection of actuator faults under windy conditions.