We systematically elucidate the optoelectronic properties of rare-earth doped and Ce co-doped yttrium aluminum garnet (YAG) using hybrid exchange-correlation functional based density functional theory. The predicted optical transitions agree with the experimental observations for single doped Ce:YAG, Pr:YAG, and co-doped Er,Ce:YAG. We find that co-doping of Ce-doped YAG with any lanthanide except Eu and Lu lowers the transition energies; we attribute this behavior to the lanthanide-induced change in bonding environment of the dopant atoms. Furthermore, we find infrared transitions only in case of the Er, Tb, and Tm co-doped Ce:YAG and suggest Tm,Ce:YAG and Tb,Ce:YAG as possible functional materials for efficient spectral up-conversion devices.