We describe the digital acquisition systems used in the EDELWEISS experiment. In the EDELWEISS-I experiment, both charge and phonon signals are continuously digitized after preamplification and transferred to a computer using a high-speed DMA channel via a 1.5Gbit/s optical fibre link, decoupling the detectors from the acquisition computer. Both phonon and charge triggers are defined numerically, without any analog triggering module, allowing a flexible filtering and trigger definition. The performances reached in this system are described, together with the improvements presently realized for the second phase of the experiment, EDELWEISS-II, involving up to 120 detectors.