To many unmanned aerial vehicle (UAV) designs, the lack of information about the wind speed and direction is a limiting factor in achieving robust outdoor flight. This paper addresses the problem of wind estimation onboard a hovering vertical take-off and landing (VTOL) tailsitter UAV. The proposed estimation framework makes use of the standard onboard sensor suite: inertial measurement unit (IMU), global positioning system (GPS) and a magnetometer. No additional airspeed sensor is needed. As a result, the autopilot is provided with an estimate of the wind velocity vector in the horizontal (north-east) plane. An aerodynamic model of the vehicle has been derived and used in a Kalman filter framework to estimate the horizontal wind velocity vector in real-time. The wind estimator has been implemented onboard the UAVs autopilot and validated in real flight. As a result, we successfully obtain the direction and speed of the wind with an estimation accuracy close to the accuracy range of the ground truth measurement. Furthermore, the derived grey-box model allows to generalise the framework to different airframes.