Drell-Yan lepton pairs produced in the process $p \bar{p} \rightarrow \ell^+\ell^- + X$ through an intermediate $\gamma^*/Z$ boson have an asymmetry in their angular distribution related to the spontaneous symmetry breaking of the electroweak force and the associated mixing of its neutral gauge bosons. The CDF and D0 experiments have measured the effective-leptonic electroweak mixing parameter $\sin^2\theta^{\rm lept}_{\rm eff}$ using electron and muon pairs selected from the full Tevatron proton-antiproton data sets collected in 2001-2011, corresponding to 9-10 fb$^{-1}$ of integrated luminosity. The combination of these measurements yields the most precise result from hadron colliders, $\sin^2 \theta^{\rm lept}_{\rm eff} = 0.23148 \pm 0.00033$. This result is consistent with, and approaches in precision, the best measurements from electron-positron colliders. The standard model inference of the on-shell electroweak mixing parameter $\sin^2\theta_W$, or equivalently the $W$-boson mass $M_W$, using the \textsc{zfitter} software package yields $\sin^2 \theta_W = 0.22324 \pm 0.00033$ or equivalently, $M_W = 80.367 \pm 0.017 \;{\rm GeV}/c^2$.