The impressive generalization performance of modern neural networks is attributed in part to their ability to implicitly memorize complex training patterns.Inspired by this, we explore a novel mechanism to improve model generalization via explicit memorization.Specifically, we propose the residual-memorization (ResMem) algorithm, a new method that augments an existing prediction model (e.g., a neural network) by fitting the model's residuals with a nearest-neighbor based regressor.The final prediction is then the sum of the original model and the fitted residual regressor.By construction, ResMem can explicitly memorize the training labels.We start by formulating a stylized linear regression problem and rigorously show that ResMem results in a more favorable test risk over a base linear neural network.Then, we empirically show that ResMem consistently improves the test set generalization of the original prediction model across standard vision and natural language processing benchmarks.