Medical image registration and segmentation are two of the most frequent tasks in medical image analysis. As these tasks are complementary and correlated, it would be beneficial to apply them simultaneously in a joint manner. In this paper, we formulate registration and segmentation as a joint problem via a Multi-Task Learning (MTL) setting, allowing these tasks to leverage their strengths and mitigate their weaknesses through the sharing of beneficial information. We propose to merge these tasks not only on the loss level, but on the architectural level as well. We studied this approach in the context of adaptive image-guided radiotherapy for prostate cancer, where planning and follow-up CT images as well as their corresponding contours are available for training. The study involves two datasets from different manufacturers and institutes. The first dataset was divided into training (12 patients) and validation (6 patients), and was used to optimize and validate the methodology, while the second dataset (14 patients) was used as an independent test set. We carried out an extensive quantitative comparison between the quality of the automatically generated contours from different network architectures as well as loss weighting methods. Moreover, we evaluated the quality of the generated deformation vector field (DVF). We show that MTL algorithms outperform their Single-Task Learning (STL) counterparts and achieve better generalization on the independent test set. The best algorithm achieved a mean surface distance of $1.06 \pm 0.3$ mm, $1.27 \pm 0.4$ mm, $0.91 \pm 0.4$ mm, and $1.76 \pm 0.8$ mm on the validation set for the prostate, seminal vesicles, bladder, and rectum, respectively. The high accuracy of the proposed method combined with the fast inference speed, makes it a promising method for automatic re-contouring of follow-up scans for adaptive radiotherapy.