The convergence of cloud computing and artificial intelligence (AI) has enabled transformative capabilities across industries, but it also introduces a complex and evolving threat landscape that demands a paradigm shift in cybersecurity strategy. This article systematically examines the multifaceted security, privacy, and integrity challenges inherent in cloud-AI integrated ecosystems. We analyze critical vulnerabilities spanning data lifecycle exposure, adversarial machine learning attacks, insecure Machine Learning Operations (MLOps) pipelines, and risks arising from shared cloud infrastructure and regulatory fragmentation. In response, the article explores a suite of intelligent, adaptive, and often AI-driven defense mechanisms designed to secure the cloud-AI stack. These include Privacy-Enhancing Technologies (PETs) such as federated learning and confidential computing, adversarial robustness techniques, Zero-Trust Architectures for MLOps, and AI-powered security orchestration for continuous threat detection and response. We argue that securing this convergence requires a holistic, proactive approach that integrates security-by-design principles throughout the AI lifecycle and leverages the cloud's own capabilities to create resilient, trustworthy, and compliant intelligent systems.