The increasing abuse of image editing software causes the authenticity of digital images questionable. Meanwhile, the widespread availability of online social networks (OSNs) makes them the dominant channels for transmitting forged images to report fake news, propagate rumors, etc. Unfortunately, various lossy operations, e.g., compression and resizing, adopted by OSNs impose great challenges for implementing the robust image forgery detection. To fight against the OSN-shared forgeries, in this work, a novel robust training scheme is proposed. Firstly, we design a baseline detector, which won the top ranking in a recent certificate forgery detection competition. Then we conduct a thorough analysis of the noise introduced by OSNs, and decouple it into two parts, i.e., predictable noise and unseen noise, which are modelled separately. The former simulates the noise introduced by the disclosed (known) operations of OSNs, while the latter is designed to not only complete the previous one, but also take into account the defects of the detector itself. We further incorporate the modelled noise into a robust training framework, significantly improving the robustness of the image forgery detector. Extensive experimental results are presented to validate the superiority of the proposed scheme compared with several state-of-the-art competitors, especially in the scenarios of detecting OSN-transmitted forgeries. Finally, to promote the future development of the image forgery detection, we build a public forgeries dataset based on four existing datasets through the uploading and downloading of four most popular OSNs. The data and code of this work are available at https://github.com/HighwayWu/ImageForensicsOSN.