Graph neural networks (GNNs) achieve the state-of-the-art on graph-relevant tasks such as node and graph classification. However, recent works show GNNs are vulnerable to adversarial perturbations include the perturbation on edges, nodes, and node features, the three components forming a graph. Empirical defenses against such attacks are soon broken by adaptive ones. While certified defenses offer robustness guarantees, they face several limitations: 1) almost all restrict the adversary's capability to only one type of perturbation, which is impractical; 2) all are designed for a particular GNN task, which limits their applicability; and 3) the robustness guarantees of all methods except one are not 100% accurate. We address all these limitations by developing AGNNCert, the first certified defense for GNNs against arbitrary (edge, node, and node feature) perturbations with deterministic robustness guarantees, and applicable to the two most common node and graph classification tasks. AGNNCert also encompass existing certified defenses as special cases. Extensive evaluations on multiple benchmark node/graph classification datasets and two real-world graph datasets, and multiple GNNs validate the effectiveness of AGNNCert to provably defend against arbitrary perturbations. AGNNCert also shows its superiority over the state-of-the-art certified defenses against the individual edge perturbation and node perturbation.