The X-ray pulsar Her X-1 was observed for more than two orbital cycles near the maximum of the 35 day X-ray intensity cycle by the Narrow Field Instruments on-board the BeppoSAX satellite. We present the first simultaneous measurement of the 0.1-200 keV spectrum. Three distinct continuum components are evident in the phase averaged spectrum: a low energy excess, modeled as a 0.1 keV blackbody; a power-law and a high energy cut-off. Superposed on this continuum are Fe L and K emission features at 1.0 and 6.5 keV, respectively, and a ~40 keV cyclotron absorption feature. The cyclotron feature can be clearly seen in raw count spectra. We present the properties of the cyclotron feature with unprecedented precision and discuss the indications given by this measurement on the physical properties of the emitting region.