Tetragonal garnet-type Li7La3Zr2O12 is an important candidate solid electrolyte for all-solid-state lithium ion batteries because of its high ionic conductivity and large electrochemical potential window. Here we employ atomistic simulation methods to show that the most favourable disorder process in Li7La3Zr2O12 involves loss of Li2O resulting in lithium and oxygen vacancies, which promote vacancy mediated self-diffusion. The activation energy for lithium migration (0.45 eV) is much lower than that for oxygen (1.65 eV). Furthermore, the oxygen migration activation energy reveals that the oxygen diffusion in this material can be facilitated at higher temperatures once oxygen vacancies form.