We present the measurement of the two-neutrino double-β decay rate of ^{76}Ge performed with the GERDA Phase II experiment. With a subset of the entire GERDA exposure, 11.8 kg yr, the half-life of the process has been determined: T_{1/2}^{2ν}=(2.022±0.018_{stat}±0.038_{syst})×10^{21} yr. This is the most precise determination of the ^{76}Ge two-neutrino double-β decay half-life and one of the most precise measurements of a double-β decay process. The relevant nuclear matrix element can be extracted: M_{eff}^{2ν}=(0.101±0.001).