Graph anomaly detection (GAD), which aims to identify nodes in a graph that significantly deviate from normal patterns, plays a crucial role in broad application domains. However, existing GAD methods are one-model-for-one-dataset approaches, i.e., training a separate model for each graph dataset. This largely limits their applicability in real-world scenarios. To overcome this limitation, we propose a novel zero-shot generalist GAD approach UNPrompt that trains a one-for-all detection model, requiring the training of one GAD model on a single graph dataset and then effectively generalizing to detect anomalies in other graph datasets without any retraining or fine-tuning. The key insight in UNPrompt is that i) the predictability of latent node attributes can serve as a generalized anomaly measure and ii) generalized normal and abnormal graph patterns can be learned via latent node attribute prediction in a properly normalized node attribute space. UNPrompt achieves a generalist mode for GAD through two main modules: one module aligns the dimensionality and semantics of node attributes across different graphs via coordinate-wise normalization, while another module learns generalized neighborhood prompts that support the use of latent node attribute predictability as an anomaly score across different datasets. Extensive experiments on real-world GAD datasets show that UNPrompt significantly outperforms diverse competing methods under the generalist GAD setting, and it also has strong superiority under the one-model-for-one-dataset setting. Code is available at https://github.com/mala-lab/UNPrompt.