The final results of the EDELWEISS-I dark matter search using cryogenic heat-and-ionization Ge detectors are presented. The final data sample corresponds to an increase by a factor five in exposure relative to the previously published results. A recoil energy threshold of 13 keV or better was achieved with three 320g detectors working simultaneously over four months of stable operation. Limits on the spin-independent cross-section for the scattering of a WIMP on a nucleon are derived from an accumulated fiducial exposure of 62 kg.d.