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Image normalization is a building block in medical image analysis. Conventional approaches are customarily utilized on a per-dataset basis. This strategy, however, prevents the current normalization algorithms from fully exploiting the complex joint information available across multiple datasets. Consequently, ignoring such joint information has a direct impact on the performance of segmentation algorithms. This paper proposes to revisit the conventional image normalization approach by instead learning a common normalizing function across multiple datasets. Jointly normalizing multiple datasets is shown to yield consistent normalized images as well as an improved image segmentation. To do so, a fully automated adversarial and task-driven normalization approach is employed as it facilitates the training of realistic and interpretable images while keeping performance on-par with the state-of-the-art. The adversarial training of our network aims at finding the optimal transfer function to improve both the segmentation accuracy and the generation of realistic images. We evaluated the performance of our normalizer on both infant and adult brains images from the iSEG, MRBrainS and ABIDE datasets. Results reveal the potential of our normalization approach for segmentation, with Dice improvements of up to 57.5% over our baseline. Our method can also enhance data availability by increasing the number of samples available when learning from multiple imaging domains.