Existing approaches for autonomous control of pan-tilt-zoom (PTZ) cameras use multiple stages where object detection and localization are performed separately from the control of the PTZ mechanisms. These approaches require manual labels and suffer from performance bottlenecks due to error propagation across the multi-stage flow of information. The large size of object detection neural networks also makes prior solutions infeasible for real-time deployment in resource-constrained devices. We present an end-to-end deep reinforcement learning (RL) solution called Eagle to train a neural network policy that directly takes images as input to control the PTZ camera. Training reinforcement learning is cumbersome in the real world due to labeling effort, runtime environment stochasticity, and fragile experimental setups. We introduce a photo-realistic simulation framework for training and evaluation of PTZ camera control policies. Eagle achieves superior camera control performance by maintaining the object of interest close to the center of captured images at high resolution and has up to 17% more tracking duration than the state-of-the-art. Eagle policies are lightweight (90x fewer parameters than Yolo5s) and can run on embedded camera platforms such as Raspberry PI (33 FPS) and Jetson Nano (38 FPS), facilitating real-time PTZ tracking for resource-constrained environments. With domain randomization, Eagle policies trained in our simulator can be transferred directly to real-world scenarios.