We report the first discovery of a multi-planetary system by the HATSouth network, HATS-59b,c, a planetary system with an inner transiting hot Jupiter and an outer cold massive giant planet, which was detected via radial velocity. The inner transiting planet, HATS-59b, is on an eccentric orbit with ℓ = 0.129 ± 0.049, orbiting a V = 13.951 ± 0.030 mag solar-like star (M∗ =1.038 ± 0.039 Mo and R∗ = 1.036 ± 0.067 Ro) with a period of 5.416081 ± 0.000016 days. The outer companion, HATS-59c is on a circular orbit with m sin i = 12.70 ± 0.87 MJ and a period of 1422 ± 14 days. The inner planet has a mass of 0.806 ± 0.069 MJ and a radius of 1.126 ± 0.077 RJ, yielding a density of 0.70 ± 0.16 g cm-3. Unlike most planetary systems that include only a single hot Jupiter, HATS-59b,c includes, in addition to the transiting hot Jupiter, a massive outer companion. The architecture of this system is valuable for understanding planet migration.