  We compute $S$-wave quarkonium wavefunctions at the origin in the
$\overline{\rm MS}$ scheme based on nonrelativistic effective field theories.
We include the effects of nonperturbative long-distance behaviors of the
potentials, while we determine the short-distance behaviors of the potentials
in perturbative QCD. We obtain $\overline{\rm MS}$-renormalized quarkonium
wavefunctions at the origin that have the correct scale dependences that are
expected from perturbative QCD, so that the scale dependences cancel in
physical quantities. Based on the calculation of the wavefunctions at the
origin, we make model-independent predictions of decay constants and
electromagnetic decay rates of $S$-wave charmonia and bottomonia, and compare
them with measurements. We find that the poor convergence of perturbative QCD
corrections are substantially improved when we include corrections to the
wavefunctions at the origin in the calculation of decay constants and decay
rates.
