In this paper the autonomous flight mode conversion control scheme for a Quad-TiltRotor Unmanned Aerial Vehicle is presented. This convertible UAV type has the capability for flying both as a helicopter as well as a fixed-wing aircraft type, by adjusting the orientation of its tilt-enabled rotors. Thus, a platform combining the operational advantages of two commonly distinct aircraft types is formed. However, its autonomous mid-flight conversion is an issue of increased complexity. The approach presented is based on an innovative control scheme, developed based on hybrid systems theory. Particularly, a piecewise affine modeling approximation of the complete nonlinear dynamics is derived and serves as the model for control over which a hybrid predictive controller that provides global stabilization, optimality and constraints satisfaction is computed. The effectiveness of the proposed control scheme in handling the mode conversion from helicopter to fixed-wing (and conversely) is demonstrated via a series of simulation studies. The proposed control scheme exceeds the functionality of the aforementioned flight-mode conversion and is also able to handle the transition to intermediate flight-modes with rotors slightly tilted forward in order to provide a forward force component while flying in close to helicopter-mode.