Gazetteers were shown to be useful resources for named entity recognition (NER). Many existing approaches to incorporating gazetteers into machine learning based NER systems rely on manually defined selection strategies or handcrafted templates, which may not always lead to optimal effectiveness, especially when multiple gazetteers are involved. This is especially the case for the task of Chinese NER, where the words are not naturally tokenized, leading to additional ambiguities. To automatically learn how to incorporate multiple gazetteers into an NER system, we propose a novel approach based on graph neural networks with a multi-digraph structure that captures the information that the gazetteers offer. Experiments on various datasets show that our model is effective in incorporating rich gazetteer information while resolving ambiguities, outperforming previous approaches.