We report the discovery and validation of two long-period giant exoplanets orbiting the early K dwarf TOI-4600 (V = 12.6, T = 11.9), first detected using observations from the Transiting Exoplanet Survey Satellite (TESS) by the TESS Single Transit Planet Candidate Working Group. The inner planet, TOI-4600 b, has a radius of 6.80 ± 0.31 R ⊕ and an orbital period of 82.69 days. The outer planet, TOI-4600 c, has a radius of 9.42 ± 0.42 R ⊕ and an orbital period of 482.82 days, making it the longest-period confirmed or validated planet discovered by TESS to date. We combine TESS photometry and ground-based spectroscopy, photometry, and high-resolution imaging to validate the two planets. With equilibrium temperatures of 347 K and 191 K, respectively, TOI-4600 b and c add to the small but growing population of temperate giant exoplanets that bridge the gap between hot/warm Jupiters and the solar system's gas giants. TOI-4600 is a promising target for further transit and precise RV observations to measure the masses and orbits of the planets as well as search for additional nontransiting planets. Additionally, with Transit Spectroscopy Metric values of ~30, both planets are amenable for atmospheric characterization with JWST. Together, these will lend insight into the formation and evolution of planet systems with multiple giant exoplanets.