Blockchain-artificial intelligence (AI) convergence is a new paradigm for safeguarding cloud computing data storage. The research introduces a hybrid model leveraging blockchain's distributed, unalterable ledger and AI's predictability to eradicate data breaches, unauthorized use, and integrity. The system registered 96.3% and 97.8% accuracy levels in anomaly detection in a test bed cloud environment and the CICIDS 2017 dataset employing Random Forest and Deep Neural Network models, respectively. On the other hand, blockchain implementation using Hyperledger Fabric reduced unauthorized data access by 85% and improved auditability by 92%. Performance testing also registered a 21% boost in system resilience and 15% lower latency than traditional models. In addition, the anomaly detection component achieved a precision of 0.93, recall of 0.88, and F1-score of 0.90, indicating a vibrant balance between detecting threats accurately and decreasing false alarms. The results establish that AI-based blockchain models significantly improve cloud storage security, suggesting an intelligent and scalable solution to the expanding world of cyber threats.