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Word-wise Fully Homomorphic Encryption (FHE) schemes, such as CKKS, are gaining significant traction due to their ability to provide post-quantum-resistant, privacy preserving approximate computing—an especially desirable feature in the Machine-Learning-as-a-Service (MLaaS) paradigm. In this work, we introduce FIDESlib, the first open-source server-side CKKS GPU library that is fully interoperable with well-established client-side OpenFHE operations. Unlike other existing open-source GPU libraries, FIDESlib provides the first implementation featuring heavily optimized GPU kernels for all CKKS primitives, including bootstrapping. Our library also integrates robust benchmarking and testing, ensuring it remains adaptable to further optimization. Comparing our scheme against Phantom (the previously top open-source CKK library, we show that FIDESlib offers superior performance and scalability. For bootstrapping, FIDESlib achieves no less than 70× speedup over the AVX-optimized OpenFHE implementation. FIDESlib is available on Github.