The atomistic structure, energetics, and electronic structure of single-substitutional Ce and La defects and double-substitutional Ce-La defects in Ce,La-codoped yttrium aluminum garnet (YAG) Y3Al5O12 have been studied by means of first-principles periodic boundary conditions density functional theory calculations. Single substitution. of Y by Ce or by La produces atomistic expansions around the impurities, which are significantly smaller than the ionic radii mismatches and the overall lattice distortions are found to be confined within their second coordination spheres. In double-substitutional defects, the impurities tend to be as close as possible. La-codoping Ce:YAG provokes an anisotropic expansion around Ce defects. The Ce impurity introduces 4f occupied states in the 5.0 eV computed gap of YAG, peaking 0.25 eV above the top of the valence band, and empty 4f, 5d, and 6s states starting at 3.8 eV in the gap and spreading over the conduction band. La-codoping produces very small effects on the electronic structure of Ce:YAG, the most visible one being the decrease in covalent bonding with one of the oxygen atoms, which shifts 0.05 angstrom away from Ce and gets 0.04 angstrom closer to La in the most stable Ce La double-substitutional defect.