Abstract The Transiting Exoplanet Survey Satellite (TESS) is continuing its second extended mission after 55 sectors of observations. TESS publishes full-frame images (FFIs) at a cadence of 1800, 600, or 200 s, allowing light curves to be extracted for stars beyond a limited number of pre-selected stars. Simulations show that thousands of exoplanets, eclipsing binaries, variable stars, and other astrophysical transients can be found in these FFI light curves. To obtain high-precision light curves, we forward model the FFI with the effective point-spread function (PSF) to remove contamination from nearby stars. We adopt star positions and magnitudes from Gaia DR3 as priors. The resulting light curves, called TESS–Gaia light curves (TGLCs), show a photometric precision closely tracking the prelaunch prediction of the noise level. The TGLCs’ photometric precision reaches ≲2% at 16th TESS magnitude even in crowded fields. We publish TGLC aperture and PSF light curves for stars down to 16th TESS magnitude through the Mikulski Archive for Space Telescopes for all available sectors and will continue to deliver future light curves. The open-source package tglc 3 3 Via 10.17909/610m‐9474. is publicly available to enable any user to produce customized light curves.