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Advancements in deep generative models have made it possible to synthesize images, videos and audio signals that are difficult to distinguish from natural signals, creating opportunities for potential abuse of these capabilities. This motivates the problem of tracking the provenance of signals, i.e., being able to determine the original source of a signal. Watermarking the signal at the time of signal creation is a potential solution, but current techniques are brittle and watermark detection mechanisms can easily be bypassed by applying post-processing transformations (cropping images, shifting pitch in the audio etc.). In this paper, we introduce ReSWAT (Resilient Signal Watermarking via Adversarial Training), a framework for learning transformation-resilient watermark detectors that are able to detect a watermark even after a signal has been through several post-processing transformations. Our detection method can be applied to domains with continuous data representations such as images, videos or sound signals. Experiments on watermarking image and audio signals show that our method can reliably detect the provenance of a signal, even if it has been through several post-processing transformations, and improve upon related work in this setting. Furthermore, we show that for specific kinds of transformations (perturbations bounded in the L2 norm), we can even get formal guarantees on the ability of our model to detect the watermark. We provide qualitative examples of watermarked image and audio samples in https://drive.google.com/open?id=1-yZ0WIGNu2Iez7UpXBjtjVgZu3jJjFga.