Hardware security verification is a challenging and time-consuming task. For this purpose, design engineers may utilize tools such as formal verification, linters, and functional simulation tests, coupled with analysis and a deep understanding of the hardware design being inspected. Large Language Models (LLMs) have been used to assist during this task, either directly or in conjunction with existing tools. We improve the state of the art by proposing MARVEL, a multi-agent LLM framework for a unified approach to decision-making, tool use, and reasoning. MARVEL mimics the cognitive process of a designer looking for security vulnerabilities in RTL code. It consists of a supervisor agent that devises the security policy of the system-on-chips (SoCs) using its security documentation. It delegates tasks to validate the security policy to individual executor agents. Each executor agent carries out its assigned task using a particular strategy. Each executor agent may use one or more tools to identify potential security bugs in the design and send the results back to the supervisor agent for further analysis and confirmation. MARVEL includes executor agents that leverage formal tools, linters, simulation tests, LLM-based detection schemes, and static analysis-based checks. We test our approach on a known buggy SoC based on OpenTitan from the Hack@DATE competition. We find that 20 of the 48 issues reported by MARVEL pose security vulnerabilities.