Depth completion aims to predict a dense depth map from a sparse depth input. The acquisition of dense ground truth annotations for depth completion settings can be difficult and, at the same time, a significant domain gap between real LiDAR measurements and synthetic data has prevented from successful training of models in virtual settings. We propose a domain adaptation approach for sparse-to-dense depth completion that is trained from synthetic data, without annotations in the real domain or additional sensors. Our approach simulates the real sensor noise in an RGB+LiDAR set-up, and consists of three modules: simulating the real LiDAR input in the synthetic domain via projections, filtering the real noisy LiDAR for supervision and adapting the synthetic RGB image using a CycleGAN approach. We extensively evaluate these modules against the state-of-the-art in the KITTI depth completion benchmark, showing significant improvements.