We investigated the electronic structure of 5d transition-metal oxide Sr2IrO4 using angle-resolved photoemission, optical conductivity, x-ray absorption measurements, and first-principles band calculations. The system was found to be well described by novel effective total angular momentum Jeff states, in which the relativistic spin-orbit coupling is fully taken into account under a large crystal field. Despite delocalized Ir 5d states, the Jeff states form such narrow bands that even a small correlation energy leads to the Jeff=1/2 Mott ground state with unique electronic and magnetic behaviors, suggesting a new class of Jeff quantum spin driven correlated-electron phenomena.