The challenge of the cloud removal task can be alleviated with the aid of Synthetic Aperture Radar (SAR) images that can penetrate cloud cover. However, the large domain gap between optical and SAR images as well as the severe speckle noise of SAR images may cause significant interference in SAR-based cloud removal, resulting in performance degeneration. In this paper, we propose a novel global–local fusion based cloud removal (GLF-CR) algorithm to leverage the complementary information embedded in SAR images. Exploiting the power of SAR information to promote cloud removal entails two aspects. The first, global fusion, guides the relationship among all local optical windows to maintain the structure of the recovered region consistent with the remaining cloud-free regions. The second, local fusion, transfers complementary information embedded in the SAR image that corresponds to cloudy areas to generate reliable texture details of the missing regions, and uses dynamic filtering to alleviate the performance degradation caused by speckle noise. Extensive evaluation demonstrates that the proposed algorithm can yield high quality cloud-free images and outperform state-of-the-art cloud removal algorithms with a gain about 1.7 dB in terms of PSNR on SEN12MS-CR dataset.