In this work we present the architecture and results of a fully digital Front End Electronics (FEE) read out system developed for the GALILEO array. The FEE system, developed in collaboration with the Advanced Gamma Tracking Array (AGATA) collaboration, is composed of three main blocks: preamplifiers, digitizers and preprocessing electronics. The slow control system contains a custom Linux driver, a dynamic library and a server implementing network services. This work presents the first results of the digital FEE system coupled with a GALILEO germanium detector, which has demonstrated the capability to achieve an energy resolution of 1.53‰ at an energy of 1.33 MeV, similar to the one obtained with a conventional analog system. While keeping a good performance in terms of energy resolution, digital electronics will allow to instrument the full GALILEO array with a versatile system with high integration and low power consumption and costs.