To exploit the full potential of multicomponent wide-bandgap oxides, an in-depth understanding of the complex defect chemistry and of the role played by the constituent oxides is required. In this work, thorough theoretical and experimental investigations are combined in order to explain the carrier generation and transport in crystalline InGaZnO4. Using first-principles density functional approach, we calculate the formation energies and transition levels of possible acceptor and donor point defects as well as the implied defect complexes in InGaZnO4 and determine the equilibrium defect and electron densities as a function of growth temperature and oxygen partial pressure. An excellent agreement of the theoretical results with our Brouwer analysis of the bulk electrical measurements for InGaZnO4 establishes the Ga antisite defect, Ga-Zn, as the major electron donor in InGaZnO4. Moreover, we show that the oxygen vacancies, long believed to be the carrier source in this oxide, are scarce. The proposed carrier generation mechanism also explains the observed intriguing behavior of the conductivity in In-rich vs Ga-rich InGaZnO4.