We propose Boundary-RL, a novel weakly supervised segmentation method that utilises only patch-level labels for training. We envision the segmentation as a boundary detection problem, rather than a pixel-level classification as in previous works. This outlook on segmentation may allow for boundary delineation under challenging scenarios such as where noise artefacts may be present within the region-of-interest (ROI) boundaries, where traditional pixel-level classification-based weakly supervised methods may not be able to effectively segment the ROI. Particularly of interest, ultrasound images, where intensity values represent acoustic impedance differences between boundaries, may also benefit from the boundary delineation approach. Our method uses reinforcement learning to train a controller function to localise boundaries of ROIs using a reward derived from a pre-trained boundary-presence classifier. The classifier indicates when an object boundary is encountered within a patch, as the controller modifies the patch location in a sequential Markov decision process. The classifier itself is trained using only binary patch-level labels of object presence, which are the only labels used during training of the entire boundary delineation framework, and serves as a weak signal to inform the boundary delineation. The use of a controller function ensures that a sliding window over the entire image is not necessary. It also prevents possible false-positive or -negative cases by minimising number of patches passed to the boundary-presence classifier. We evaluate our proposed approach for a clinically relevant task of prostate gland segmentation on trans-rectal ultrasound images. We show improved performance compared to other tested weakly supervised methods, using the same labels e.g., multiple instance learning.