We report the discovery of two transiting extrasolar planets by the HATSouth survey. HATS-9b orbits an old (10.8 + or - 1.5 Gyr) V = 13.3 G dwarf star with a period P approximately 1.9153 days. The host star has a mass of 1.03 M sub(odot), radius of 1.503 Rodot, and effective temperature 5366 + or - 70 K. The planetary companion has a mass of 0.837 M sub(J) and radius of 1.065 R sub(J), yielding a mean density of 0.85 g cm super(-3). HATS-10b orbits a V = 13.1 G dwarf star with a period P approximately 3.3128 days. The host star has a mass of 1.1 M sub(odot), radius of 1.11 R sub(odot), and effective temperature 5880 + or - 120 K. The planetary companion has a mass of 0.53 M sub(J) and radius of 0.97 R sub(J), yielding a mean density of 0.7 g cm super(-3). Both planets are compact in comparison with planets receiving similar irradiation from their host stars and lie in the nominal coordinates of Field 7 of K2, but only HATS-9b falls on working silicon. Future characterization of HATS-9b with the exquisite photometric precision of the Kepler telescope may provide measurements of its reflected light signature.