Social conventions are the foundation for social and economic life. As legions of AI agents increasingly interact with each other and with humans, their ability to form shared conventions will determine how effectively they will coordinate behaviors, integrate into society and influence it. Here, we investigate the dynamics of conventions within populations of Large Language Model (LLM) agents using simulated interactions. First, we show that globally accepted social conventions can spontaneously arise from local interactions between communicating LLMs. Second, we demonstrate how strong collective biases can emerge during this process, even when individual agents appear to be unbiased. Third, we examine how minority groups of committed LLMs can drive social change by establishing new social conventions. We show that once these minority groups reach a critical size, they can consistently overturn established behaviors. In all cases, contrasting the experimental results with predictions from a minimal multi-agent model allows us to isolate the specific role of LLM agents. Our results clarify how AI systems can autonomously develop norms without explicit programming and have implications for designing AI systems that align with human values and societal goals.