The interpretation of prostate MRI suffers from low agreement across radiologists due to the subtle differences between cancer and normal tissue. Image registration addresses this issue by accurately mapping the ground-truth cancer labels from surgical histopathology images onto MRI. Cancer labels achieved by image registration can be used to improve radiologists' interpretation of MRI by training deep learning models for early detection of prostate cancer. A major limitation of current automated registration approaches is that they require manual prostate segmentations, which is a time-consuming task, prone to errors. This paper presents a weakly supervised approach for affine and deformable registration of MRI and histopathology images without requiring prostate segmentations. We used manual prostate segmentations and mono-modal synthetic image pairs to train our registration networks to align prostate boundaries and local prostate features. Although prostate segmentations were used during the training of the network, such segmentations were not needed when registering unseen images at inference time. We trained and validated our registration network with 135 and 10 patients from an internal cohort, respectively. We tested the performance of our method using 16 patients from the internal cohort and 22 patients from an external cohort. The results show that our weakly supervised method has achieved significantly higher registration accuracy than a state-of-the-art method run without prostate segmentations. Our deep learning framework will ease the registration of MRI and histopathology images by obviating the need for prostate segmentations.