Unprocessed RAW data is a highly valuable image format for image editing and computer vision. However, since the file size of RAW data is huge, most users can only get access to processed and compressed sRGB images. To bridge this gap, we design an Invertible Image Signal Processing (InvISP) pipeline, which not only enables rendering visually appealing sRGB images but also allows recovering nearly perfect RAW data. Due to our framework's inherent reversibility, we can reconstruct realistic RAW data instead of synthesizing RAW data from sRGB images, without any memory overhead. We also integrate a differentiable JPEG compression simulator that empowers our framework to reconstruct RAW data from JPEG images. Extensive quantitative and qualitative experiments on two DSLR demonstrate that our method obtains much higher quality in both rendered sRGB images and reconstructed RAW data than alternative methods.