The extragalactic background light (EBL) is the diffuse radiation with the
second highest energy density in the Universe after the cosmic microwave
background. The aim of this study is the measurement of the imprint of the EBL
opacity to gamma-rays on the spectra of the brightest extragalactic sources
detected with the High Energy Stereoscopic System (H.E.S.S.). The originality
of the method lies in the joint fit of the EBL optical depth and of the
intrinsic spectra of the sources, assuming intrinsic smoothness. Analysis of a
total of ~10^5 gamma-ray events enables the detection of an EBL signature at
the 8.8 std dev level and constitutes the first measurement of the EBL optical
depth using very-high energy (E>100 GeV) gamma-rays. The EBL flux density is
constrained over almost two decades of wavelengths (0.30-17 microns) and the
peak value at 1.4 micron is derived as 15 +/- 2 (stat) +/- 3 (sys) nW / m^2 sr.
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