Motion artifacts are a primary source of magnetic resonance (MR) image quality deterioration with strong repercussions on diagnostic performance. Currently, MR motion correction is carried out either prospectively, with the help of motion tracking systems, or retrospectively by mainly utilizing computationally expensive iterative algorithms. In this paper, we utilize a new adversarial framework, titled MedGAN, for the joint retrospective correction of rigid and non-rigid motion artifacts in different body regions and without the need for a reference image. MedGAN utilizes a unique combination of non-adversarial losses and a new generator architecture to capture the textures and fine-detailed structures of the desired artifact-free MR images. Quantitative and qualitative comparisons with other adversarial techniques have illustrated the proposed model performance.