We performed first-principles calculations of the momentum distributions of annihilating electron-positron pairs in vacancies in uranium dioxide. Full atomic relaxation effects (due to both electronic and positronic forces) were taken into account and self-consistent two-component density functional theory schemes were used. We present one-dimensional momentum distributions (Doppler-broadened annihilation radiation line shapes) along with line-shape parameters S and W. We studied the effect of the charge state of the defect on the Doppler spectra. The effect of krypton incorporation in the vacancy was also considered and it was shown that it should be possible to observe the fission gas incorporation in defects in UO2 using positron annihilation spectroscopy. We suggest that the Doppler broadening measurements can be especially useful for studying impurities and dopants in UO2 and of mixed actinide oxides.