Enterprises increasingly distribute workloads across multiple public cloud providers to optimize cost, resilience, and regulatory reach. This heterogeneity fragments security and regulatory controls, making periodic, manual audits inadequate for maintaining a defensible compliance posture. This paper presents a framework for continuous compliance automation that treats regulatory and security controls as executable policy and enforces them across heterogeneous cloud environments without human intervention in the steady state. We describe a layered architecture comprising a unified control-mapping model, a policy-as-code authoring layer, a continuous evaluation engine that ingests configuration and runtime telemetry, and an automated remediation subsystem that resolves drift against a declared baseline. A prototype evaluation across three major cloud providers indicates that continuous evaluation reduces the mean time to detect control violations from days to minutes and materially lowers manual audit effort. We conclude by examining open challenges in cross-provider normalization, false-positive management, and the governance of autonomous remediation.