Large Language Models (LLMs) have experienced rapid advancements, with applications spanning a wide range of fields, including sentiment classification, review generation, and question answering. Due to their efficiency and versatility, researchers and companies increasingly employ LLM-generated data to train their models. However, the inability to track content produced by LLMs poses a significant challenge, potentially leading to copyright infringement for the LLM owners. In this paper, we propose a method for injecting watermarks into LLM-generated datasets, enabling the tracking of downstream tasks to detect whether these datasets were produced using the original LLM. These downstream tasks can be divided into two categories. The first involves using the generated datasets at the input level, commonly for training classification tasks. The other is the output level, where model trainers use LLM-generated content as output for downstream tasks, such as question-answering tasks. We design a comprehensive set of experiments to evaluate both watermark methods. Our results indicate the high effectiveness of our watermark approach. Additionally, regarding model utility, we find that classifiers trained on the generated datasets achieve a test accuracy exceeding 0.900 in many cases, suggesting that the utility of such models remains robust. For the output-level watermark, we observe that the quality of the generated text is comparable to that produced using real-world datasets. Through our research, we aim to advance the protection of LLM copyrights, taking a significant step forward in safeguarding intellectual property in this domain.