We present the final combination of CDF and D0 measurements of cross sections for single-top-quark production in proton-antiproton collisions at a center-of-mass energy of 1.96 TeV. The data correspond to total integrated luminosities of up to 9.7 fb^{-1} per experiment. The t-channel cross section is measured to be σ_{t}=2.25_{-0.31}^{+0.29} pb. We also present the combinations of the two-dimensional measurements of the s- vs t-channel cross section. In addition, we give the combination of the s+t channel cross section measurement resulting in σ_{s+t}=3.30_{-0.40}^{+0.52} pb, without assuming the standard model value for the ratio σ_{s}/σ_{t}. The resulting value of the magnitude of the top-to-bottom quark coupling is |V_{tb}|=1.02_{-0.05}^{+0.06}, corresponding to |V_{tb}|>0.92 at the 95% C.L.