Blimps are well suited to perform long-duration aerial tasks as they are energy efficient, relatively silent and safe. To address the blimp navigation and control task, in previous work we developed a hardware and software-in-the-loop framework and a PID-based controller for large blimps in the presence of wind disturbance. However, blimps have a deformable structure and their dynamics are inherently non-linear and time-delayed, making PID controllers difficult to tune. Thus, often resulting in large tracking errors. Moreover, the buoyancy of a blimp is constantly changing due to variations in ambient temperature and pressure. To address these issues, in this paper we present a learning-based framework based on deep residual reinforcement learning (DRRL), for the blimp control task. Within this framework, we first employ a PID controller to provide baseline performance. Subsequently, the DRRL agent learns to modify the PID decisions by interaction with the environment. We demonstrate in simulation that DRRL agent consistently improves the PID performance. Through rigorous simulation experiments, we show that the agent is robust to changes in wind speed and buoyancy. In real-world experiments, we demonstrate that the agent, trained only in simulation, is sufficiently robust to control an actual blimp in windy conditions. We openly provide the source code of our approach at https://github.com/ robot-perception-group/AutonomousBlimpDRL.