Few-shot segmentation is a challenging dense prediction task, which entails segmenting a novel query image given only a small annotated support set. The key problem is thus to design a method that aggregates detailed information from the support set, while being robust to large variations in appearance and context. To this end, we propose a few-shot segmentation method based on dense Gaussian process (GP) regression. Given the support set, our dense GP learns the mapping from local deep image features to mask values, capable of capturing complex appearance distributions. Furthermore, it provides a principled means of capturing uncertainty, which serves as another powerful cue for the final segmentation, obtained by a CNN decoder. Instead of a one-dimensional mask output, we further exploit the end-to-end learning capabilities of our approach to learn a high-dimensional output space for the GP. Our approach sets a new state-of-the-art for both 1-shot and 5-shot FSS on the PASCAL-5i and COCO-20i benchmarks, achieving an absolute gain of +14.9 mIoU in the COCO-20i 5-shot setting. Furthermore, the segmentation quality of our approach scales gracefully when increasing the support set size, while achieving robust cross-dataset transfer.