DarkSide-50 is a detector for dark matter candidates in the form of weakly interacting massive particles. It utilizes a liquid argon time projection chamber for the inner main detector, surrounded by a liquid scintillator veto (LSV) and a water Cherenkov veto detector (WCV). The LSV and WCV act as the neutron and cosmogenic muon veto detectors for DarkSide-50. This paper describes the electronics and data acquisition system used for these two detectors. The system is made of a custom built front end electronics and commercial National Instruments high speed digitizers. The front end electronics, the DAQ, and the trigger system have been used to acquire data in the form of zero-suppressed waveform samples from the 110 PMTs of the LSV and the 80 PMTs of the WCV. The veto DAQ system has proven its performance and reliability. This electronics and DAQ system can be scaled and used as it is for the veto of the next generation DarkSide-20k detector.