Deep Learning has achieved tremendous results by pushing the frontier of automation in diverse domains. Unfortunately, current neural network architectures are not explainable by design. In this paper, we propose a novel method that trains deep hypernetworks to generate explainable linear models. Our models retain the accuracy of black-box deep networks while offering free lunch explainability by design. Specifically, our explainable approach requires the same runtime and memory resources as black-box deep models, ensuring practical feasibility. Through extensive experiments, we demonstrate that our explainable deep networks are as accurate as state-of-the-art classifiers on tabular data. On the other hand, we showcase the interpretability of our method on a recent benchmark by empirically comparing prediction explainers. The experimental results reveal that our models are not only as accurate as their black-box deep-learning counterparts but also as interpretable as state-of-the-art explanation techniques.