TOI-2202 b is a transiting warm Jovian-mass planet with an orbital period of P = 11.91 days identified from the Full Frame Images data of five different sectors of the TESS mission. Ten TESS transits of TOI-2202 b combined with three follow-up light curves obtained with the CHAT robotic telescope show strong transit timing variations (TTVs) with an amplitude of about 1.2 hr. Radial velocity follow-up with FEROS, HARPS, and PFS confirms the planetary nature of the transiting candidate (a b = 0.096 ± 0.001 au, m b = 0.98 ± 0.06 M Jup), and a dynamical analysis of RVs, transit data, and TTVs points to an outer Saturn-mass companion (a c = 0.155 ± 0.002 au, m c = 0.37 ± 0.10 M Jup) near the 2:1 mean motion resonance. Our stellar modeling indicates that TOI-2202 is an early K-type star with a mass of 0.82 M ⊙, a radius of 0.79 R ⊙, and solar-like metallicity. The TOI-2202 system is very interesting because of the two warm Jovian-mass planets near the 2:1 mean motion resonance, which is a rare configuration, and their formation and dynamical evolution are still not well understood. *Based on observations collected at the European Organization for Astronomical Research in the Southern Hemisphere under ESO programs 0104.C-0413 and 1102.C-0923, and MPG programs 0102.A-9006, 0103.A-9008, and 0104.A-9007. This paper includes data gathered with the 6.5 meter Magellan Telescopes located at Las Campanas Observatory, Chile.