21 pages, 5 figuresThe EDELWEISS-II collaboration has completed a direct search for WIMP dark matter with an array of ten 400-g cryogenic germanium detectors in operation at the Laboratoire Souterrain de Modane. The combined use of thermal phonon sensors and charge collection electrodes with an interleaved geometry enables the efficient rejection of gamma-induced radioactivity as well as near-surface interactions. A total effective exposure of 384 kg.d has been achieved, mostly coming from fourteen months of continuous operation. Five nuclear recoil candidates are observed above 20 keV, while the estimated background is less than 3.0 events. The result is interpreted in terms of limits on the cross-section of spin-independent interactions of WIMPs and nucleons. A cross-section of 4.4x10^-8 pb is excluded at 90%CL for a WIMP mass of 85 GeV. New constraints are also set on models where the WIMP-nucleon scattering is inelastic