Early Exit Neural Networks (EENNs) present a solution to enhance the efficiency of neural network deployments. However, creating EENNs is challenging and requires specialized domain knowledge, due to the large amount of additional design choices. To address this issue, we propose an automated augmentation flow that focuses on converting an existing model into an EENN. It performs all required design decisions for the deployment to heterogeneous or distributed hardware targets: Our framework constructs the EENN architecture, maps its subgraphs to the hardware targets, and configures its decision mechanism. To the best of our knowledge, it is the first framework that is able to perform all of these steps. We evaluated our approach on a collection of Internet-of-Things and standard image classification use cases. For a speech command detection task, our solution was able to reduce the mean operations per inference by 59.67%. For an ECG classification task, it was able to terminate all samples early, reducing the mean inference energy by 74.9% and computations by 78.3%. On CIFAR-10, our solution was able to achieve up to a 58.75% reduction in computations. The search on a ResNet-152 base model for CIFAR-10 took less than nine hours on a laptop CPU. Our proposed approach enables the creation of EENN optimized for IoT environments and can reduce the inference cost of Deep Learning applications on embedded and fog platforms, while also significantly reducing the search cost - making it more accessible for scientists and engineers in industry and research. The low search cost improves the accessibility of EENNs, with the potential to improve the efficiency of neural networks in a wide range of practical applications.