Earth and Moon are shown here to be composed of oxygen isotope reservoirs that are indistinguishable, with a difference in {Delta}17O of -1 +/- 5ppm (2se). Based on these data and our new planet formation simulations that include a realistic model for oxygen isotopic reservoirs, our results favor vigorous mixing during the giant impact and therefore a high-energy high- angular-momentum impact. The results indicate that the late veneer impactors had an average {Delta}17O within approximately 1 per mil of the terrestrial value, suggesting that these impactors were water rich.