This paper presents the mathematical modeling, controller design, and flight-testing of an over-actuated Vertical Take-off and Landing (VTOL) tiltwing Unmanned Aerial Vehicle (UAV). Based on simplified aerodynamics and first-principles, a dynamical model of the UAV is developed which captures key aerodynamic effects including propeller slipstream on the wing and post-stall characteristics of the airfoils. The model-based steady-state flight envelope and the corresponding trim-actuation is analyzed and the overactuation of the UAV solved by optimizing for, e.g., power-optimal trims. The developed control system is composed of two controllers: First, a low-level attitude controller based on dynamic inversion and a daisy-chaining approach to handle allocation of redundant actuators. Secondly, a higher-level cruise controller to track a desired vertical velocity. It is based on a linearization of the system and look-up tables to determine the strong and nonlinear variation of the trims throughout the flight-envelope. We demonstrate the performance of the controlsystem for all flight phases (hover, transition, cruise) in extensive flight-tests.