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 $9.7\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ per experiment. The $t$-channel cross section is measured to be ${\ensuremath{\sigma}}_{t}=2.2{5}_{\ensuremath{-}0.31}^{+0.29}\text{ }\text{ }\mathrm{pb}$. 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 ${\ensuremath{\sigma}}_{s+t}=3.3{0}_{\ensuremath{-}0.40}^{+0.52}\text{ }\text{ }\mathrm{pb}$, without assuming the standard model value for the ratio ${\ensuremath{\sigma}}_{s}/{\ensuremath{\sigma}}_{t}$. The resulting value of the magnitude of the top-to-bottom quark coupling is $|{V}_{tb}|=1.0{2}_{\ensuremath{-}0.05}^{+0.06}$, corresponding to $|{V}_{tb}|>0.92$ at the 95% C.L.