Dynamic contrast-enhanced quantitative first-pass perfusion using magnetic resonance imaging enables non-invasive objective assessment of myocardial ischemia without ionizing radiation. However, quantification of perfusion is challenging due to the non-linearity between the magnetic resonance signal intensity and contrast agent concentration. Furthermore, respiratory motion during data acquisition precludes quantification of perfusion. While motion correction techniques have been proposed, they have been hampered by the challenge of accounting for dramatic contrast changes during the bolus and long execution times. In this work we investigate the use of a novel free-breathing multi-echo Dixon technique for quantitative myocardial perfusion. The Dixon fat images, unaffected by the dynamic contrast-enhancement, are used to efficiently estimate rigid-body respiratory motion and the computed transformations are applied to the corresponding diagnostic water images. This is followed by a second non-linear correction step using the Dixon water images to remove residual motion. The proposed Dixon motion correction technique was compared to the state-of-the-art technique (spatiotemporal based registration). We demonstrate that the proposed method performs comparably to the state-of-the-art but is significantly faster to execute. Furthermore, the proposed technique can be used to correct for the decay of signal due to T2* effects to improve quantification and additionally, yields fat-free diagnostic images.