Normal fetal adipose tissue (AT) development is essential for perinatal well-being. AT, or simply fat, stores energy in the form of lipids. Malnourishment may result in excessive or depleted adiposity. Although previous studies showed a correlation between the amount of AT and perinatal outcome, prenatal assessment of AT is limited by lacking quantitative methods. Using magnetic resonance imaging (MRI), 3D fat-and water-only images of the entire fetus can be obtained from twopoint Dixon images to enable AT lipid quantification. This paper is the first to present a methodology for developing a deep learning (DL) based method for fetal fat segmentation based on Dixon MRI. It optimizes radiologists' manual fetal fat delineation time to produce annotated training dataset. It consists of two steps: 1) model-based semi-automatic fetal fat segmentations, reviewed and corrected by a radiologist; 2) automatic fetal fat segmentation using DL networks trained on the resulting annotated dataset. Segmentation of 51 fetuses was performed with the semi-automatic method. Three DL networks were trained. We show a significant improvement in segmentation times (3:38 hours → < 1 hour) and observer variability (Dice of 0.738 → 0.906) compared to manual segmentation. Automatic segmentation of 24 test cases with the 3D Residual U-Net, nn-UNet and SWIN-UNetR transformer networks yields a mean Dice score of 0.863, 0.787 and 0.856, respectively. These results are better than the manual observer variability, and comparable to automatic adult and pediatric fat segmentation. A radiologist reviewed and corrected six new independent cases segmented using the best performing network (3D Residual U-Net), resulting in a Dice score of 0.961 and a significantly reduced correction time of 15:20 minutes. Using these novel segmentation methods and short MRI acquisition time, whole body subcutaneous lipids can be quantified for individual fetuses in the clinic and large-cohort research.