This paper develops a hybrid control strategy that provides autonomous transition between hovered and leveled flights to a model-scale fixed-wing aircraft. The aircraft's closed-loop dynamics are described by means of a hybrid automaton with the hover, transition, level, and recovery operating modes, each one corresponding to a different region of the flight envelope. Linear parameter varying control techniques are employed in hover and level, providing robust local stabilization, and a nonlinear locally input-to-state stable controller provides practical reference tracking to the transition operating mode. These controllers, together with an appropriate choice of reference maneuvers, ensure that a transition from hovered flight to level flight, or vice versa, is achieved. Whenever the aircraft state reaches unexpected values, the recovery controller is triggered in order to drive the aircraft toward stable hovered flight, providing a chance to retry the transition maneuver. The controllers' performance and robustness is assessed within a realistic simulation environment in the presence of sensor noise.