Ensuring the security of complex system-on-chips (SoCs) designs is a critical imperative, yet traditional verification techniques struggle to keep pace due to significant challenges in automation, scalability, comprehensiveness, and adaptability. The advent of large language models (LLMs), with their remarkable capabilities in natural language understanding, code generation, and advanced reasoning, presents a new paradigm for tackling these issues. Moving beyond monolithic models, an agentic approach allows for the creation of multi-agent systems where specialized LLMs collaborate to solve complex problems more effectively. Recognizing this opportunity, we introduce SV-LLM, a novel multi-agent assistant system designed to automate and enhance SoC security verification. By integrating specialized agents for tasks like verification question answering, security asset identification, threat modeling, test plan and property generation, vulnerability detection, and simulation-based bug validation, SV-LLM streamlines the workflow. To optimize their performance in these diverse tasks, agents leverage different learning paradigms, such as in-context learning, fine-tuning, and retrieval-augmented generation (RAG). The system aims to reduce manual intervention, improve accuracy, and accelerate security analysis, supporting proactive identification and mitigation of risks early in the design cycle. We demonstrate its potential to transform hardware security practices through illustrative case studies and experiments that showcase its applicability and efficacy.