The XENON100 experiment, located at the Laboratori Nazionali del Gran Sasso (LNGS), aims to directly detect dark matter in the form of Weakly Interacting Massive Particles (WIMPs) via their elastic scattering off xenon nuclei. We present a comprehensive study of the predicted electronic recoil background coming from radioactive decays inside the detector and shield materials, and intrinsic contamination. Based on GEANT4 Monte Carlo simulations using a detailed geometry together with the measured radioactivity of all detector components, we predict an electronic recoil background in the WIMP-search energy range (0-100 keV) in the 30 kg fiducial mass of less than 10e-2 events/(kg-day-keV), consistent with the experiments design goal. The predicted background spectrum is in very good agreement with the data taken during the commissioning of the detector, in Fall 2009.