Deep learning models are increasingly deployed to edge devices for real-time applications. To ensure stable service quality across diverse edge environments, it is highly desirable to generate tailored model architectures for different conditions. However, conventional pre-deployment model generation approaches are not satisfactory due to the difficulty of handling the diversity of edge environments and the demand for edge information. In this paper, we propose to adapt the model architecture after deployment in the target environment, where the model quality can be precisely measured and private edge data can be retained. To achieve efficient and effective edge model generation, we introduce a pretraining-assisted on-cloud model elastification method and an edge-friendly on-device architecture search method. Model elastification generates a high-quality search space of model architectures with the guidance of a developer-specified oracle model. Each subnet in the space is a valid model with different environment affinity, and each device efficiently finds and maintains the most suitable subnet based on a series of edge-tailored optimizations. Extensive experiments on various edge devices demonstrate that our approach is able to achieve significantly better accuracy-latency tradeoffs (e.g. 46.74% higher on average accuracy with a 60% latency budget) than strong baselines with minimal overhead (13 GPU hours in the cloud and 2 minutes on the edge server).