The paper discusses a deep reinforcement learning (RL) control strategy for fully autonomous vision-based approach and landing of vertical take-off and landing (VTOL) capable unmanned aerial vehicles (UAVs) on ships in the presence of disturbances such as wind gusts. The automation closely follows the Navy helicopter ship landing procedure and therefore, it detects a horizon bar that is installed on most Navy ships as a visual aid for pilots by applying uniquely developed computer vision techniques. The vision system utilizes the detected corners of the horizon bar and its known dimensions to estimate the relative position and heading angle of the aircraft. A deep RL-based controller was coupled with the vision system to ensure a safe and robust approach and landing at the proximity of the ship where the airflow is highly turbulent. The vision and RL-based control system was implemented on a quadrotor UAV and flight tests were conducted where the UAV approached and landed on a sub-scale ship platform undergoing 6 degrees of freedom deck motions in the presence of wind gusts. Simulations and flight tests confirmed the superior disturbance rejection capability of the RL controller when subjected to sudden 5 m/s wind gusts in different directions. Specifically, it was observed during flight tests that the deep RL controller demonstrated a 50% reduction in lateral drift from the flight path and 3 times faster disturbance rejection in comparison to a nonlinear proportional-integral-derivative controller.