We describe the on-board electronics chain and the on-ground data processing pipeline that will operate on data from the Herschel-SPIRE photometer to produce calibrated astronomical products. Data from the three photometer arrays will be conditioned and digitised by on-board electronics and sent to the ground with no further on-board data processing. On the ground, the data pipeline will process the data from point source, jiggle-map, and scan-map observations in a fully automatic manner, producing measured flux densities (for point source observations) or maps. It includes calculation of the bolometer voltages from the raw telemetry, glitch removal, and corrections for various effects including time constants associated with the detectors and electronics, electrical and optical crosstalk, detector temperature drifts, flatfielding, and non-linear response of the bolometers to strong sources. Flux density calibration will be with respect to standard astronomical sources with the planets Uranus and Neptune being adopted as the baseline primary standards. The pipeline will compute estimated values of in-beam flux density for a standard flat νS(ν) source spectrum.