Generative retrieval (GR) reformulates information retrieval (IR) by framing it as the generation of document identifiers (docids), thereby enabling end-to-end optimization and seamless integration with generative language models (LMs). Despite notable progress under supervised training, GR still struggles to generalize to zero-shot IR scenarios, which are prevalent in real-world applications. To tackle this challenge, we propose ZeroGR, a zero-shot generative retrieval framework that uses natural language instructions to extend GR across a wide range of IR tasks. Specifically, ZeroGR is composed of three key components: (i) an LM-based docid generator that unifies heterogeneous documents (e.g., text, tables, code) into semantically meaningful docids; (ii) an instruction-tuned query generator that generates diverse types of queries from natural language task descriptions to enhance corpus indexing; and (iii) a reverse annealing decoding strategy to balance precision and recall during docid generation. Furthermore, we introduce OpenInstIR, the most diverse open-source instructed retrieval dataset. We investigate the impact of instruction fine-tuning scale and find that performance consistently improves as the number of IR tasks encountered during training increases. Extensive experiments on the BEIR and MAIR benchmarks demonstrate that ZeroGR achieves competitive performance across a wide range of retrieval tasks, establishing a new state-of-the-art among GR methods. Our code is available at https://github.com/sunnweiwei/ZeroGR.