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 hours. Radial velocity follow-up with FEROS, HARPS and PFS confirms the planetary nature of the transiting candidate (a$_{rm b}$ = 0.096 $pm$ 0.002 au, m$_{rm b}$ = 0.98 $pm$ 0.06 M$_{rm Jup}$), and dynamical analysis of RVs, transit data, and TTVs points to an outer Saturn-mass companion (a$_{rm c}$ = 0.155 $pm$ 0.003 au, m$_{rm c}$= $0.37 pm 0.10$ M$_{rm Jup}$) 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$_odot$, a radius of 0.79 R$_odot$, and solar-like metallicity. The TOI-2202 system is very interesting because of the two warm Jovian-mass planets near the 2:1 MMR, which is a rare configuration, and their formation and dynamical evolution are still not well understood.