Given a graph learning task, such as link prediction, on a new graph, how can we select the best method as well as its hyperparameters (collectively called a model) without having to train or evaluate any model on the new graph? Model selection for graph learning has been largely ad hoc. A typical approach has been to apply popular methods to new datasets, but this is often suboptimal. On the other hand, systematically comparing models on the new graph quickly becomes too costly, or even impractical. In this work, we develop the first meta-learning approach for evaluation-free graph learning model selection, called MetaGL, which utilizes the prior performances of existing methods on various benchmark graph datasets to automatically select an effective model for the new graph, without any model training or evaluations. To quantify similarities across a wide variety of graphs, we introduce specialized meta-graph features that capture the structural characteristics of a graph. Then we design G-M network, which represents the relations among graphs and models, and develop a graph-based meta-learner operating on this G-M network, which estimates the relevance of each model to different graphs. Extensive experiments show that using MetaGL to select a model for the new graph greatly outperforms several existing meta-learning techniques tailed for graph learning model selection (up to 47% better), while being extremely fast at test time (∼1 sec).