The recent advancement of large foundation models (FMs) has increased the demand for fine-tuning these models on large-scale and cross-domain datasets. To address this, federated fine-tuning has emerged as a solution, allowing models to be fine-tuned on distributed datasets across multiple devices while ensuring data privacy. However, the substantial parameter size of FMs and the multi-round communication required by traditional federated fine-tuning algorithms result in prohibitively high communication costs, challenging the practicality of federated fine-tuning. In this paper, we are the first to reveal, both theoretically and empirically, that the traditional multi-round aggregation algorithms may not be necessary for federated fine-tuning large FMs. Our experiments reveal that a single round of communication (i.e., one-shot federated fine-tuning) yields a global model performance comparable to that achieved through multiple rounds of communication. Through rigorous mathematical and empirical analyses, we demonstrate that large FMs, due to their extensive parameter sizes and pre-training on general tasks, achieve significantly lower training loss in one-shot federated fine-tuning compared to smaller models. Our extensive experiments show that one-shot federated fine-tuning not only reduces communication costs but also enables asynchronous aggregation, enhances privacy, and maintains performance consistency with multi-round federated fine-tuning for models larger than 1 billion parameters, on text generation and text-to-image generation tasks. Our findings have the potential to revolutionize federated fine-tuning in practice, enhancing efficiency, reducing costs, and expanding accessibility for large-scale models. This breakthrough paves the way for broader adoption and application of federated fine-tuning across various domains.