We introduce RoboMorph, an automated approach for generating and optimizing modular robot designs using large language models (LLMs) and evolutionary algorithms. In this framework, we represent each robot design as a grammar and leverage the capabilities of LLMs to navigate the extensive robot design space, which is traditionally time-consuming and computationally demanding. By integrating automatic prompt design and a reinforcement learning based control algorithm, RoboMorph iteratively improves robot designs through feedback loops. Our experimental results demonstrate that RoboMorph can successfully generate nontrivial robots that are optimized for a single terrain while showcasing improvements in morphology over successive evolutions. Our approach demonstrates the potential of using LLMs for data-driven and modular robot design, providing a promising methodology that can be extended to other domains with similar design frameworks.