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Hybrid storage systems (HSS) use multiple different storage devices to provide high and scalable storage capacity at high performance. Recent research proposes various techniques that aim to accurately identify performance-critical data to place it in a "best-fit" storage device. Unfortunately, most of these techniques are rigid, which (1) limits their adaptivity to perform well for a wide range of workloads and storage device configurations, and (2) makes it difficult for designers to extend these techniques to different storage system configurations (e.g., with a different number or different types of storage devices) than the configuration they are designed for. We introduce Sibyl, the first technique that uses reinforcement learning for data placement in hybrid storage systems. Sibyl observes different features of the running workload as well as the storage devices to make system-aware data placement decisions. For every decision it makes, Sibyl receives a reward from the system that it uses to evaluate the long-term performance impact of its decision and continuously optimizes its data placement policy online. We implement Sibyl on real systems with various HSS configurations. Our results show that Sibyl provides 21.6%/19.9% performance improvement in a performance-oriented/cost-oriented HSS configuration compared to the best previous data placement technique. Our evaluation using an HSS configuration with three different storage devices shows that Sibyl outperforms the state-of-the-art data placement policy by 23.9%-48.2%, while significantly reducing the system architect's burden in designing a data placement mechanism that can simultaneously incorporate three storage devices. We show that Sibyl achieves 80% of the performance of an oracle policy that has complete knowledge of future access patterns while incurring a very modest storage overhead of only 124.4 KiB.