We report the discovery of four short-period extrasolar planets transiting moderately bright stars from photometric measurements of the HATSouth network coupled to additional spectroscopic and photometric follow-up observations. While the planet masses range from 0.26 to 0.90 M-J, the radii are all approximately a Jupiter radii, resulting in a wide range of bulk densities. The orbital period of the planets ranges from 2.7 days to 4.7 days, with HATS-43b having an orbit that appears to be marginally non-circular (e = 0.173 +/- 0.089). HATS-44 is notable for having a high metallicity ([Fe/H]= 0.320 +/- 0.071). The host stars spectral types range from late F to early K, and all of them are moderately bright (13.3 < V < 14.4), allowing the execution of future detailed follow-up observations. HATS-43b and HATS-46b, with expected transmission signals of 2350 ppm and 1500 ppm, respectively, are particularly well suited targets for atmospheric characterization via transmission spectroscopy.