Differentially Private Federated Learning (DP-FL) has garnered attention as a collaborative machine learning approach that ensures formal privacy. Most DP-FL approaches ensure DP at the record-level within each silo for cross-silo FL. However, a single user's data may extend across multiple silos, and the desired user-level DP guarantee for such a setting remains unknown. In this study, we present Uldp-FL, a novel FL framework designed to guarantee user-level DP in cross-silo FL where a single user's data may belong to multiple silos. Our proposed algorithm directly ensures user-level DP through per-user weighted clipping, departing from group-privacy approaches. We provide a theoretical analysis of the algorithm's privacy and utility. Additionally, we enhance the utility of the proposed algorithm with an enhanced weighting strategy based on user record distribution and design a novel private protocol that ensures no additional information is revealed to the silos and the server. Experiments on real-world datasets show substantial improvements in our methods in privacy-utility trade-offs under user-level DP compared to baseline methods. To the best of our knowledge, our work is the first FL framework that effectively provides user-level DP in the general cross-silo FL setting.