Very-high-energy (VHE; E >100 GeV) and high-energy (HE; 100 MeV < E < 100 GeV) data from gamma-ray observations performed with the H.E.S.S. telescope array and the Fermi-LAT instrument, respectively, are analysed in order to investigate the non-thermal processes in the starburst galaxy NGC 253. The VHE gamma-ray data can be described by a power law in energy with differential photon index Gamma=2.14 pm 0.18_stat pm 0.30_sys and differential flux normalisation at 1 TeV of F_0 = (9.6 pm 1.5_stat (+5.7,-2.9)_sys) x 10^{-14} TeV^{-1} cm^{-2} s^{-1}. A power-law fit to the differential HE gamma-ray spectrum reveals a photon index of Gamma=2.24 pm 0.14_stat pm 0.03_sys and an integral flux between 200 MeV and 200 GeV of F(0.2-200 GeV) = (4.9 pm 1.0_stat pm 0.3_sys) x 10^{-9} cm^{-2} s^{-1}. No evidence for a spectral break or turnover is found over the dynamic range of both the LAT instrument and the H.E.S.S. experiment: a combined fit of a power law to the HE and VHE gamma-ray data results in a differential photon index Gamma=2.34 pm 0.03 with a p-value of 30%. The gamma-ray observations indicate that at least about 20% of the energy of the cosmic rays capable of producing hadronic interactions is channeled into pion production. The smooth alignment between the spectra in the HE and VHE gamma-ray domain suggests that the same transport processes dominate in the entire energy range. Advection is most likely responsible for charged particle removal from the starburst nucleus from GeV to multiple TeV energies. In a hadronic scenario for the gamma-ray production, the single overall power-law spectrum observed would therefore correspond to the mean energy spectrum produced by the ensemble of cosmic-ray sources in the starburst region.
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