In this work we present a deep learning solution for motion correction in brain MRI; specifically we approach motion correction as an image synthesis problem. Motion is simulated in previously acquired brain images; the image pairs (corrupted + original) are used to train a conditional generative adversarial network (cGAN), referred to as MoCo-cGAN, to predict artefact-free images from motion-corrupted data. We also demonstrate transfer learning, where the network is fine-tuned to apply motion correction to images with a different contrast. The trained MoCo-cGAN successfully performed motion correction on brain images with simulated motion. All predicted images were quantitatively improved, and significant artefact suppression was observed.