We introduce HyperMorph, a framework that facilitates efficient hyperparameter tuning in learning-based deformable image registration. Classical registration algorithms perform an iterative pair-wise optimization to compute a deformation field that aligns two images. Recent learning-based approaches leverage large image datasets to learn a function that rapidly estimates a deformation for a given image pair. In both strategies, the accuracy of the resulting spatial correspondences is strongly influenced by the choice of certain hyperparameter values. However, an effective hyperparameter search consumes substantial time and human effort as it often involves training multiple models for different fixed hyperparameter values and may lead to suboptimal registration. We propose an amortized hyperparameter learning strategy to alleviate this burden by learning the impact of hyperparameters on deformation fields. We design a meta network, or hypernetwork, that predicts the parameters of a registration network for input hyperparameters, thereby comprising a single model that generates the optimal deformation field corresponding to given hyperparameter values. This strategy enables fast, high-resolution hyperparameter search at test-time, reducing the inefficiency of traditional approaches while increasing flexibility. We also demonstrate additional benefits of HyperMorph, including enhanced robustness to model initialization and the ability to rapidly identify optimal hyperparameter values specific to a dataset, modality, task, or even anatomical region, all without the need to retrain models.