H.E.S.S.—the high energy stereoscopic system—is a new system of large atmospheric Cherenkov telescopes for GeV/TeV astronomy. Each of the four telescopes of 107m2 mirror area is equipped with a 960-pixel photomultiplier-tube camera. This paper describes the methods used to convert the photomultiplier signals into the quantities needed for Cherenkov image analysis. Two independent calibration techniques have been applied in parallel to provide an estimation of uncertainties. Results on the long-term stability of the H.E.S.S. cameras are also presented.