  We determine the strong coupling constant $\alpha_s$ from the static QCD
potential by matching a theoretical calculation with a lattice QCD computation.
We employ a new theoretical formulation based on the operator product
expansion, in which renormalons are subtracted from the leading Wilson
coefficient. We remove not only the leading renormalon uncertainty of
$\mathcal{O}(\Lambda_{\rm QCD})$ but also the first $r$-dependent uncertainty
of $\mathcal{O}(\Lambda_{\rm QCD}^3 r^2)$. The theoretical prediction for the
potential turns out to be valid at the static color charge distance
$\Lambda_{\rm \overline{MS}} r \lesssim 0.8$ ($r \lesssim 0.4$ fm), which is
significantly larger than ordinary perturbation theory. With lattice data down
to $\Lambda_{\rm \overline{MS}} r \sim 0.09$ ($r \sim 0.05$ fm), we perform the
matching in a wide region of $r$, which has been difficult in previous
determinations of $\alpha_s$ from the potential. Our final result is
$\alpha_s(M_Z^2) = 0.1179^{+0.0015}_{-0.0014}$ with 1.3 % accuracy. The
dominant uncertainty comes from higher order corrections to the perturbative
prediction and can be straightforwardly reduced by simulating finer lattices.
