COSINE-100 is a dark matter direct detection experiment designed to test the annual modulation signal observed by the DAMA/LIBRA experiment. COSINE-100 consists of 8 NaI(Tl) crystals with a total mass of 106 kg, a 2200 L liquid scintillator veto, and 37 muon detector panels. We present details of the data acquisition system of COSINE-100, including waveform storage using flash analog-to-digital converters for crystal events and integrated charge storage using charge-sensitive analog-to-digital converters for liquid scintillator and plastic scintillator muon veto events. We also discuss several trigger conditions developed in order to distinguish signal events from photomultiplier noise events. The total trigger rate observed for the crystal/liquid scintillator (plastic scintillator) detector is 15 Hz (24 Hz).