Medical image segmentation is the process of anatomically isolating organs for analysis and treatment. Leading works within this domain emerged with the well-known U-Net. Despite its success, recent works have shown the limitations of U-Net to conduct segmentation given image particularities such as noise, corruption or lack of contrast. Prior knowledge integration allows to overcome segmentation ambiguities. This paper introduces BB-UNet (Bounding Box U-Net), a deep learning model that integrates location as well as shape prior onto model training. The proposed model is inspired by U-Net and incorporates priors through a novel convolutional layer introduced at the level of skip connections. The proposed architecture helps in presenting attention kernels onto the neural training in order to guide the model on where to look for the organs. Moreover, it fine-tunes the encoder layers based on positional constraints. The proposed model is exploited within two main paradigms: as a solo model given a fully supervised framework and as an ancillary model, in a weakly supervised setting. In the current experiments, manual bounding boxes are fed at inference and as such BB-Unet is exploited in a semi-automatic setting; however, BB-Unet has the potential of being part of a fully automated process, if it relies on a preliminary step of object detection. To validate the performance of the proposed model, experiments are conducted on two public datasets: the SegTHOR dataset which focuses on the segmentation of thoracic organs at risk in computed tomography (CT) images, and the Cardiac dataset which is a mono-modal MRI dataset released as part of the Decathlon challenge and dedicated to segmentation of the left atrium. Results show that the proposed method outperforms state-of-the-art methods in fully supervised learning frameworks and registers relevant results given the weakly supervised domain.