Graph anomaly detection (GAD) aims to identify abnormal nodes that differ from the majority of the nodes in a graph, which has been attracting significant attention in recent years. Existing generalist graph models have achieved remarkable success in different graph tasks but struggle to generalize to the GAD task. This limitation arises from their difficulty in learning generalized knowledge for capturing the inherently infrequent, irregular and heterogeneous abnormality patterns in graphs from different domains. To address this challenge, we propose AnomalyGFM, a GAD-oriented graph foundation model that supports zero-shot inference and few-shot prompt tuning for GAD in diverse graph datasets. One key insight is that graph-agnostic representations for normal and abnormal classes are required to support effective zero/few-shot GAD across different graphs. Motivated by this, AnomalyGFM is pre-trained to align data-independent, learnable normal and abnormal class prototypes with node representation residuals (i.e., representation deviation of a node from its neighbors). The residual features essentially project the node information into a unified feature space where we can effectively measure the abnormality of nodes from different graphs in a consistent way. This provides a driving force for the learning of graph-agnostic, discriminative prototypes for the normal and abnormal classes, which can be used to enable zero-shot GAD on new graphs, including very large-scale graphs. If there are few-shot labeled normal nodes available in the new graphs, AnomalyGFM can further support prompt tuning to leverage these nodes for better adaptation. Comprehensive experiments on 11 widely-used GAD datasets with real anomalies, demonstrate that AnomalyGFM significantly outperforms state-of-the-art competing methods under both zero- and few-shot GAD settings.