Using a dataset of 6.32 fb^{-1} of e^{+}e^{-} annihilation data collected with the BESIII detector at center-of-mass energies between 4178 and 4226 MeV, we have measured the absolute branching fraction of the leptonic decay D_{s}^{+}→τ^{+}ν_{τ} via τ^{+}→e^{+}ν_{e}ν[over ¯]_{τ}, and find B_{D_{s}^{+}→τ^{+}ν_{τ}}=(5.27±0.10±0.12)×10^{-2}, where the first uncertainty is statistical and the second is systematic. The precision is improved by a factor of 2 compared to the previous best measurement. Combining with f_{D_{s}^{+}} from lattice quantum chromodynamics calculations or the |V_{cs}| from the CKMfitter group, we extract |V_{cs}|=0.978±0.009±0.012 and f_{D_{s}^{+}}=(251.1±2.4±3.0) MeV, respectively. Combining our result with the world averages of B_{D_{s}^{+}→τ^{+}ν_{τ}} and B_{D_{s}^{+}→μ^{+}ν_{μ}}, we obtain the ratio of the branching fractions B_{D_{s}^{+}→τ^{+}ν_{τ}}/B_{D_{s}^{+}→μ^{+}ν_{μ}}=9.72±0.37, which is consistent with the standard model prediction of lepton flavor universality.