A giant impact between the proto-Earth and a Mars-sized impactor named Theia is the favoured scenario for the formation of the Moon. Oxygen isotopic compositions have been found to be identical between terrestrial and lunar samples, which is inconsistent with numerical models estimating that more than 40% of the Moon-forming disk material was derived from Theia. However, it remains uncertain whether more refractory elements, such as titanium, show the same degree of isotope homogeneity as oxygen in the Earth-Moon system. Here we present 50Ti/47Ti ratios in lunar samples measured by mass spectrometry. After correcting for secondary effects associated with cosmic-ray exposure at the lunar surface using samarium and gadolinium isotope systematics, we find that the 50Ti/47Ti ratio of the Moon is identical to that of the Earth within about four parts per million, which is only 1/150 of the isotopic range documented in meteorites. The isotopic homogeneity of this highly refractory element suggests that lunar material was derived from the proto-Earth mantle, an origin that could be explained by efficient impact ejection, by an exchange of material between the Earth's magma ocean and the protolunar disk, or by fission from a rapidly rotating post-impact Earth.