G349.7+0.2 is a young Galactic supernova remnant (SNR) located at the distance of 11.5 kpc and observed across the entire electromagnetic spectrum from radio to high energy (HE) Gamma-rays. Radio and infrared observations indicate that the remnant is interacting with a molecular cloud. In this paper, the detection of very high energy (VHE) Gamma-ray emission coincident with this SNR with the High Energy Stereoscopic System (H.E.S.S.) is reported. An integral flux F(E>400GeV)=(6.5 +-1.1stat +-1.3syst) x 10^{-13} ph/cm/s corresponding to 0.7% of that of the Crab Nebula and to a luminosity of 10^34 erg/s above the same energy threshold, and a steep photon index Gamma_VHE = 2.8 +-0.27stat +-0.20syst are measured. The analysis of more than 5 yr of Fermi-LAT data towards this source shows a power-law like spectrum with a best-fit photon index Gamma_HE = 2.2 +-0.04stat +0.13-0.31syst. The combined Gamma-ray spectrum of G349.7+0.2 can be described by either a broken power-law (BPL) or a power-law with exponential (or sub-exponential) cutoff (PLC). In the former case, the photon break energy is found at E_br,gamma = 55 +70-30 GeV, slightly higher than what is usually observed in the HE/VHE Gamma-ray emitting middle-aged SNRs known to be interacting with molecular clouds. In the latter case, the exponential (respectively sub-exponential) cutoff energy is measured at E_cut,gamma = 1.4 +1.6-0.55 (respectively 0.35 +0.75-0.21) TeV. A pion-decay process resulting from the interaction of the accelerated protons and nuclei with the dense surrounding medium is clearly the preferred scenario to explain the Gamma-ray emission. The BPL with a spectral steepening of 0.5-1 and the PLC provide equally good fits to the data. The product of the average gas density and the total energy content of accelerated protons and nuclei amounts to nH Wp ~ 5 x 10^51 erg/cm3.
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