The Gamma Ray Energy Tracking In-Beam Nuclear Array (GRETINA), a germanium detector system capable of measuring energy and position (within better than 2 mm rms) of gamma-ray interaction points and tracking multiple gamma-ray interactions, has been built. GRETINA is composed of seven detector modules, each with four high purity germanium crystals. Four custom designed electronics support the operation of the detectors: Digitizer/Digital Signal Processing (DSP), Trigger/Timing, Breakout Chassis and the Detector Interface Box. The Digitizer/DSP converts the analog information with 14-bit analog to digital converters operating at 100 MS/s, and digitally processes the data to determine the energy and timing information of the gamma interactions within a crystal. The computing system is composed of VME readout CPUs running VxWorks, which communicate with 62 dual-processor farm (each processor with four cores) through a 10 Gb/s Ethernet switch. The CPUs read out the digitizer/DSPs and send the data to the farm. The processors compute the position and track of the interactions of the gamma-ray inside the crystals. The processor farm is capable of processing in real-time the position of 20 000 gamma-ray/s. In this paper we will present the details of the implementation and performance of the electronics and computing system of GRETINA.