The supernova remnant (SNR) W49B originated from a core-collapse supernova that occurred between one and four thousand years ago, and subsequently evolved into a mixed-morphology remnant, which is interacting with molecular clouds (MC). $gamma$-ray observations of SNR/MC associations are a powerful tool to constrain the origin of Galactic cosmic-rays, as they can probe the acceleration of hadrons through their interaction with the surrounding medium and subsequent emission of non-thermal photons. The detection of a $gamma$-ray source coincident with W49B at very high energies (VHE; E > 100 GeV) with the H.E.S.S. Cherenkov telescopes is reported together with a study of the source with 5 years of Fermi-LAT high energy $gamma$-ray (0.06 - 300 GeV) data. The smoothly-connected combined source spectrum, measured from 60 MeV to multi-TeV energies, shows two significant spectral breaks at $304pm20$ MeV and $8.4_{-2.5}^{+2.2}$ GeV, the latter being constrained by the joint fit from the two instruments. The detected spectral features are similar to those observed in several other SNR/MC associations and are found to be indicative of $gamma$-ray emission produced through neutral-pion decay.