The high-frequency peaked BL Lac PKS 2005-489 (z=0.071) was observed in 2003 and 2004 with the H.E.S.S. stereoscopic array of imaging atmospheric-Cherenkov telescopes in Namibia. A signal was detected at the 6.7 sigma level in the 2004 observations (24.2 hrs live time), but not in the 2003 data set (27.3 hrs live time). PKS 2005-489 is the first blazar independently discovered by H.E.S.S. to be an emitter of VHE photons, and only the second such blazar in the Southern Hemisphere. The integral flux above 200 GeV observed in 2004 is (6.9 +/- 1.0 +/- 1.4) x 10−12 cm−2 s−1, corresponding to ~2.5% of the flux observed from the Crab Nebula. The 99% upper limit on the flux in 2003, I(>200 GeV) < 5.2 x 10−12 cm−2 s−1, is smaller than the flux measured in 2004, suggesting an increased level of activity in 2004. However, the data show no evidence for significant variability on any time scale less than a year. An energy spectrum is measured and is characterized by a very soft power law (photon index = 4.0 +/- 0.4)