This Letter presents results of a search for the mixing of a sub-eV sterile neutrino with three active neutrinos based on the full data sample of the Daya Bay Reactor Neutrino Experiment, collected during 3158 days of detector operation, which contains 5.55×10^{6} reactor ν[over ¯]_{e} candidates identified as inverse beta-decay interactions followed by neutron capture on gadolinium. The analysis benefits from a doubling of the statistics of our previous result and from improvements of several important systematic uncertainties. No significant oscillation due to mixing of a sub-eV sterile neutrino with active neutrinos was found. Exclusion limits are set by both Feldman-Cousins and CLs methods. Light sterile neutrino mixing with sin^{2}2θ_{14}≳0.01 can be excluded at 95% confidence level in the region of 0.01 eV^{2}≲|Δm_{41}^{2}|≲0.1 eV^{2}. This result represents the world-leading constraints in the region of 2×10^{-4} eV^{2}≲|Δm_{41}^{2}|≲0.2 eV^{2}.