In-context learning is the ability of a pretrained model to adapt to novel and diverse downstream tasks by conditioning on prompt examples, without optimizing any parameters. While large language models have demonstrated this ability, how in-context learning could be performed over graphs is unexplored. In this paper, we develop Pretraining Over Diverse In-Context Graph Systems (PRODIGY), the first pretraining framework that enables in-context learning over graphs. The key idea of our framework is to formulate in-context learning over graphs with a novel \emph{prompt graph} representation, which connects prompt examples and queries. We then propose a graph neural network architecture over the prompt graph and a corresponding family of in-context pretraining objectives. With PRODIGY, the pretrained model can directly perform novel downstream classification tasks on unseen graphs via in-context learning. We provide empirical evidence of the effectiveness of our framework by showcasing its strong in-context learning performance on tasks involving citation networks and knowledge graphs. Our approach outperforms the in-context learning accuracy of contrastive pretraining baselines with hard-coded adaptation by 18\% on average across all setups. Moreover, it also outperforms standard finetuning with limited data by 33\% on average with in-context learning.