Generative recommendation based on Large Language Models (LLMs) have transformed the traditional ranking-based recommendation style into a text-to-text generation paradigm. However, in contrast to standard NLP tasks that inherently operate on human vocabulary, current research in generative recommendations struggles to effectively encode recommendation items within the text-to-text framework using concise yet meaningful ID representations. To better align LLMs with recommendation needs, we propose IDGen, representing each item as a unique, concise, semantically rich, platform-agnostic textual ID using human language tokens. This is achieved by training a textual ID generator alongside the LLM-based recommender, enabling seamless integration of personalized recommendations into natural language generation. Notably, as user history is expressed in natural language and decoupled from the original dataset, our approach suggests the potential for a foundational generative recommendation model. Experiments show that our framework consistently surpasses existing models in sequential recommendation under standard experimental setting. Then, we explore the possibility of training a foundation recommendation model with the proposed method on data collected from 19 different datasets and tested its recommendation performance on 6 unseen datasets across different platforms under a completely zero-shot setting. The results show that the zero-shot performance of the pre-trained foundation model is comparable to or even better than some traditional recommendation models based on supervised training, showing the potential of the IDGen paradigm serving as the foundation model for generative recommendation. Code and data are open-sourced at https://github.com/agiresearch/IDGenRec.