We report the discovery of two short-period massive giant planets from NASA's Transiting Exoplanet Survey Satellite (TESS). Both systems, TOI-558 (TIC 207110080) and TOI-559 (TIC 209459275), were identified from the 30 minute cadence full-frame images and confirmed using ground-based photometric and spectroscopic follow-up observations from TESS's follow-up observing program working group. We find that TOI-558 b, which transits an F-dwarf (M* = ${1.349}_{-0.065}^{+0.064}$ M⊙, R* = ${1.496}_{-0.040}^{+0.042}$ R⊙, Teff = ${6466}_{-93}^{+95}$ K, age ${1.79}_{-0.73}^{+0.91}$ Gyr) with an orbital period of 14.574 days, has a mass of 3.61 ± 0.15 MJ, a radius of ${1.086}_{-0.038}^{+0.041}$ RJ, and an eccentric (e = ${0.300}_{-0.020}^{+0.022}$) orbit. TOI-559 b transits a G dwarf (M* = 1.026 ± 0.057 M⊙, R* = ${1.233}_{-0.026}^{+0.028}$ R⊙, Teff = ${5925}_{-76}^{+85}$ K, age ${6.8}_{-2.0}^{+2.5}$ Gyr) in an eccentric (e = 0.151 ± 0.011) 6.984 days orbit with a mass of ${6.01}_{-0.23}^{+0.24}$ MJ and a radius of ${1.091}_{-0.025}^{+0.028}$ RJ. Our spectroscopic follow up also reveals a long-term radial velocity trend for TOI-559, indicating a long-period companion. The statistically significant orbital eccentricity measured for each system suggests that these planets migrated to their current location through dynamical interactions. Interestingly, both planets are also massive (>3 MJ), adding to the population of massive giant planets identified by TESS. Prompted by these new detections of high-mass planets, we analyzed the known mass distribution of hot and warm Jupiters but find no significant evidence for multiple populations. TESS should provide a near magnitude-limited sample of transiting hot Jupiters, allowing for future detailed population studies.