Magnitude signal-based fitting of chemical shift-encoded data enables proton density fat fraction (PDFF) and R2* estimation where complex signal-based fitting fails or when phase data are inaccessible/unreliable, such as in multicentre studies. However, traditional magnitude-based fitting suffers from Rician noise-related bias and fat-water swaps, limiting utility. Here, we propose MAGORINO, an algorithm combining Magnitude-Only PDFF and R2* estimation with Rician Noise modelling, to address these limitations. We demonstrate that MAGORINO outperforms traditional Gaussian noise-based magnitude-only estimation through (i) reduced noise-related bias and (ii) reduced fat-water swaps. This may be valuable in multicentre studies or when phase data are otherwise inaccessible/unreliable.