We present DASPack, a high-performance, open-source compression tool specifically designed for distributed acoustic sensing (DAS) data. As DAS becomes a key technology for real-time, high-density, and long-range monitoring in fields such as geophysics, infrastructure surveillance, and environmental sensing, the volume of collected data is rapidly increasing. Large-scale DAS deployments already generate hundreds of terabytes and are expected to increase in the coming years, making long-term storage a major challenge. Despite this urgent need, few compression methods have proven to be both practical and scalable in real-world scenarios. DASPack is a fully operational solution that consistently outperforms existing techniques for DAS data. It enables both controlled lossy and lossless compression by allowing users to choose the maximum absolute difference per datum between the original and compressed data. The compression pipeline combines wavelet transforms, linear predictive coding, and entropy coding to optimise efficiency. Our method achieves up to 3x file size reductions for strain and strain rate data in lossless mode across diverse datasets. In lossy mode, compression improves to 6x with near-perfect signal fidelity, and up to 10x is reached with acceptable signal degradation. It delivers fast throughput (100-200 MB/s using a single-thread and up to 750 MB/s using 8-threads), enabling real-time deployment even under high data rates. We validated its performance on 15 datasets from a variety of acquisition environments, demonstrating its speed, robustness, and broad applicability. DASPack provides a practical foundation for long-term, sustainable DAS data management in large-scale monitoring networks.