We present the first analysis of spectroscopic and photometric observations of the two southern eclipsing binary stars, V349 Ara and V4403 Sgr. Radial velocity curves of these two systems obtained at the South African Astronomical Observatory and their V light curves from the All Sky Automated Survey were solved simultaneously using the Wilson-Devinney code. Our photometric models describe these two systems as Algol-like binary stars with detached configurations. The masses and radii were found to be 2.59 +/- 0.07 M, 3.60 +/- 0.07 R and 2.51 +/- 0.06 M, 4.15 +/- 0.07 R for the primary and secondary components of V349 Ara, respectively. Those of V4403 Sgr were derived to be 1.33 +/- 0.02 M, 1.74 +/- 0.02 R and 1.59 +/- 0.03 M, 2.50 +/- 0.03 R for the primary and secondary components, respectively. The distances to V349 Ara and V4403 Sgr were computed to be 677 +/- 36 and 199 +/- 10 pc from the dynamic parallax, respectively, taking into account interstellar extinction. The evolution cases of these two systems are also examined. Both components of these two systems are evolved main-sequence stars, and the dynamic ages were estimated as approximately 0.67 and 2.29 Gyr for V349 Ara and V4403 Sgr, respectively, when compared to Geneva theoretical evolution models.