We present a comprehensive characterization of the on-orbit imaging performance of the three telescopes on board the Imaging X-ray Polarimetry Explorer (IXPE). Each telescope comprises a Wolter-I mirror module assembly and a Gas Pixel Detector focal-plane detector unit (DU). We analyze data from point-like X-ray sources and fit a composite point spread function (PSF) model that we compare with ground calibrations. We study the dependence of the PSF parameters and of the angular resolution, in terms of half-power diameter (HPD), on the time and source counting rate. We find no significant secular evolution of PSF parameters or HPD over 30 months on orbit, with average HPDs of $26.1 \pm 0.5$ arcsec (Telescope 1), $32.1 \pm 0.5$ arcsec (Telescope 2), and $30.9 \pm 0.6$ arcsec (Telescope 3), and rate trends consistent with zero up to source counting rates of $\sim60$ cts s$^{-1}$ in the 2-3 keV energy band for all three telescopes. We set a 99% C.L. upper limit of 4.4% on the optics-induced polarization in the PSF halo, and find no measurable degradation of the polarization modulation factor in the wings versus the core due to mis-reconstructed photoelectron tracks. IXPE's imaging performance thus is consistent with the $\leq30$ arcsec observatory requirement with high stability, ensuring robust spatially resolved polarization measurements for the mission's projected lifetime through 2030.
