Collecting a large number of reliable training images annotated by multiple land-cover class labels in the framework of multi-label classification is time-consuming and costly in remote sensing (RS). To address this problem, publicly available thematic products are often used for annotating RS images with zero-labeling-cost. However, such an approach may result in constructing a training set with noisy multi-labels, distorting the learning process. To address this problem, we propose a Consensual Collaborative Multi-Label Learning (CCML) method. The proposed CCML identifies, ranks and corrects training images with noisy multi-labels through four main modules: 1) discrepancy module; 2) group lasso module; 3) flipping module; and 4) swap module. The discrepancy module ensures that the two networks learn diverse features, while obtaining the same predictions. The group lasso module detects the potentially noisy labels by estimating the label uncertainty based on the aggregation of two collaborative networks. The flipping module corrects the identified noisy labels, whereas the swap module exchanges the ranking information between the two networks. The experimental results confirm the success of the proposed CCML under high (synthetically added) multi-label noise rates. The code of the proposed method is publicly available at https://noisy-labels-in-rs.org/