Airborne wind energy (AWE) is an innovative renewable energy technology, with the potential to substantially reduce the cost of energy. This paper introduces a solution for one of the main challenges of AWE systems, which is the automated reliable launching of the airborne system component. Our launch system configuration consists of a rigid-wing flying object (aircraft) equipped with a VTOL subsystem and launched vertically, with the fuselage also directed vertically. We formulate the Transition phase as an optimal control problem, so as to determine the optimal control inputs which constitute the control surface deflections and the thrust force; which steers the aircraft from hovering with its nose upwards to forward flight. Subsequently, we simulate the trajectory for two cases of optimality; (a) minimizing the power consumption and (b) minimizing the endurance, during this phase. Choosing the case of minimizing power is more reasonable for our application, as the time interval difference between the two cases is almost 3 seconds only, but with a huge difference in the power consumed. We present a detailed mathematical analysis of the system followed by extensive simulation results.