Prostate cancer is one of the main diseases affecting men worldwide. The gold standard for diagnosis and prognosis is the Gleason grading system. In this process, pathologists manually analyze prostate histology slides under microscope, in a high time-consuming and subjective task. In the last years, computer-aided-diagnosis (CAD) systems have emerged as a promising tool that could support pathologists in the daily clinical practice. Nevertheless, these systems are usually trained using tedious and prone-to-error pixel-level annotations of Gleason grades in the tissue. To alleviate the need of manual pixel-wise labeling, just a handful of works have been presented in the literature. Motivated by this, we propose a novel weakly-supervised deep-learning model, based on self-learning CNNs, that leverages only the global Gleason score of gigapixel whole slide images during training to accurately perform both, grading of patch-level patterns and biopsy-level scoring. To evaluate the performance of the proposed method, we perform extensive experiments on three different external datasets for the patch-level Gleason grading, and on two different test sets for global Grade Group prediction. We empirically demonstrate that our approach outperforms its supervised counterpart on patch-level Gleason grading by a large margin, as well as state-of-the-art methods on global biopsy-level scoring. Particularly, the proposed model brings an average improvement on the Cohen's quadratic kappa (k) score of nearly 18% compared to full-supervision for the patch-level Gleason grading task.