With the development of manufacturing technologies, topology optimization has emerged as an effective methodology for structural design. Despite its usefulness, topology optimization often requires expert knowledge for problem formulation, implementation, execution, and result interpretation, which has largely confined its use to experts. To lower this barrier, recent advances in large language models (LLMs) have led to active research on interpreting and solving scientific problems expressed in natural language. Furthermore, collaboration among multiple LLM-based agents has enabled end-to-end frameworks to address complex mechanical problems described in natural language via physics-based simulation. To the best of our knowledge, there have been few end-to-end approaches that solve topology optimization problems specified in natural language, which are particularly challenging due to the complexity and domain-specific nature of topology optimization. In this study, we present TopOptAgents, an LLM-driven multi-agent framework for topology optimization. The framework implements an iterative workflow among multiple specialized agents: a Scientist agent converts the natural-language prompt into a numerical problem description, a Planner agent outlines the implementation steps, a Coder agent generates FEniCS/pyOptSparse-based Python code, an Executor agent runs the pipeline, and a Debugger agent iteratively resolves runtime errors to produce an optimized structure. In addition, a multimodal LLM-based agent evaluates the resulting structure along with the convergence history and autonomously adjusts the optimization parameters to improve the outcomes. We evaluated TopOptAgents on several 2D benchmark problems described in underspecified natural language to validate the capability of our framework to translate them into numerical formulations with various objective functions and to produce physically plausible optimized structures. The multi-agent collaboration achieves a higher success rate in producing feasible designs than a single LLM, extending the potential of LLMs to improve the accessibility of the topology optimization process for non-experts.