We report the discovery and confirmation of two new hot Jupiters discovered by the Transiting Exoplanet Survey Satellite (TESS): TOI 564 b and TOI 905 b. The transits of these two planets were initially observed by TESS with orbital periods of 1.651 and 3.739 days, respectively. We conducted follow-up observations of each system from the ground, including photometry in multiple filters, speckle interferometry, and radial velocity measurements. For TOI 564 b, our global fitting revealed a classical hot Jupiter with a mass of ${1.463}_{-0.096}^{+0.10}$ MJ and a radius of ${1.02}_{-0.29}^{+0.71}$ RJ. Also a classical hot Jupiter, TOI 905 b has a mass of ${0.667}_{-0.041}^{+0.042}$ MJ and radius of ${1.171}_{-0.051}^{+0.053}$ RJ. Both planets orbit Sun-like, moderately bright, mid-G dwarf stars with V ∼ 11. While TOI 905 b fully transits its star, we found that TOI 564 b has a very high transit impact parameter of ${0.994}_{-0.049}^{+0.083}$ , making it one of only ∼20 known systems to exhibit a grazing transit and one of the brightest host stars among them. Therefore, TOI 564 b is one of the most attractive systems to search for additional nontransiting, smaller planets by exploiting the sensitivity of grazing transits to small changes in inclination and transit duration over a timescale of several years.