A series of Tb3+-doped Sr2YTaO6 double perovskite phosphors (SYT:Tb3+) were synthesized using a conventional solid-state reaction method. A strong green emission was observed in the SYT:Tb3+ phosphors, and the optimal doping concentration of Tb3+ was confirmed to be 5 mol%. The electric dipole-dipole interaction was ascribed to be the main mechanism for the luminescence concentration quenching. Analysis of the concentration-dependent fluorescence decay confirmed that the self-generated quenching model holds for the dynamic process of Tb3+ decays in SYT. Furthermore, the internal quantum efficiencies, non-radiative transition rates, and energy transfer rates of the 5D4 level for the SYT:Tb3+ samples were estimated, respectively. The luminescence thermal stability of the sample was also evaluated based on the Arrhenius model. The chromaticity shift of the SYT:5 mol% Tb3+ phosphor was examined to be 0.013 when the sample temperature was increased from 303 to 483 K, thus indicating excellent chromaticity shifting resistance under high temperature conditions. Moreover, the Judd-Ofelt parameters were calculated from the emission spectra of SYT:Tb3+ to be Ω2 = 0.29 × 10-20, Ω4 = 0.45 × 10-20, and Ω6 = 0.72 × 10-20 cm2, respectively. The fluorescence branching ratios and radiative transition rates for the 5D4 level were calculated based on the obtained Judd-Ofelt parameters. Finally, a white light-emitting diode (LED) prototype was assembled using a 310 nm LED chip combined with a prepared green SYT:Tb3+ phosphor and two other commercial blue and red phosphors. The obtained warm white light exhibits good chromaticity coordinates (0.32, 0.32) and a high color rendering index of 96.1. Based on the above results, it can be known that the prepared SYT:Tb3+ phosphors have a potential application as green emitting phosphors in white LEDs.