Cloud networks face increasing cyber threats, making efficient intrusion detection and alert correlation essential for maintaining security. Traditional Intrusion Detection Systems (IDS), such as rule-based and signature-based methods, suffer from high false positives, limited anomaly detection capabilities, and scalability issues in dynamic cloud environments. To address these gaps, this paper proposes an LSTM-GRU-based Intrusion Detection and Alert Correlation System, leveraging deep learning to enhance cloud security. Unlike conventional methods, our approach integrates temporal analysis (LSTM) and computational efficiency (GRU) to detect sophisticated attacks while minimizing processing overhead. The model achieves 96.8% detection accuracy, a 94.5% anomaly detection rate, and 89% alert correlation efficiency, significantly reducing redundant security notifications. Additionally, the system processes each network packet in 7.5ms, ensuring ≤10ms cloud latency impact, making it suitable for real-time applications. Comparative analysis against AES-based encryption highlights its superior efficiency in real-time intrusion detection, as encryption alone lacks proactive threat identification. The proposed framework outperforms baseline IDS models such as CNN, traditional LSTM, and rule-based systems, offering higher accuracy, lower false alarm rates, and improved scalability. This advancement enhances Security Operations Center (SOC) efficiency, reduces alert fatigue, and improves cloud resilience against emerging threats. The findings demonstrate that deep learning-driven intrusion detection is more adaptive and responsive to modern cyber threats in cloud environments. Future work will focus on incorporating federated learning to enhance security in distributed cloud infrastructures while maintaining computational efficiency.