PKS 0625-354 (z = 0.055) was observed with the four High Energy Stereoscopic System (H.E.S.S.) telescopes in 2012 during 5.5 h. The source was detected above an energy threshold of 200 GeV at a significance level of 6.1 sigma. No significant variability is found in these observations. The source is well described with a power-law spectrum with photon index Gamma = 2.84 +/- 0.50(stat) +/- 0.10(syst) and normalization (at E-0 = 1.0 TeV) N-0(E-0)=(0.58 +/- 0.22(stat) +/- 0.12(syst)) x 10(-12) TeV-1 cm(-2) s(-1). Multiwavelength data collected with Fermi-LAT, Swift-XRT, Swift-UVOT, ATOM and WISE are also analysed. Significant variability is observed only in the Fermi-LAT gamma-ray and Swift-XRT X-ray energy bands. Having a good multiwavelength coverage from radio to very high energy, we performed a broad-band modelling from two types of emission scenarios. The results from a one zone lepto-hadronic and a multizone leptonic models are compared and discussed. On the grounds of energetics, our analysis favours a leptonic multizone model. Models associated to the X-ray variability constraint support previous results, suggesting a BL Lac nature of PKS 0625-354 with, however, a large-scale jet structure typical of a radio galaxy.