  The $\pi^0$ pole constitutes the lowest-lying singularity of the hadronic
light-by-light (HLbL) tensor, and thus provides the leading contribution in a
dispersive approach to HLbL scattering in the anomalous magnetic moment of the
muon $(g-2)_\mu$. It is unambiguously defined in terms of the doubly-virtual
pion transition form factor, which in principle can be accessed in its entirety
by experiment. We demonstrate that, in the absence of a direct measurement, the
full space-like doubly-virtual form factor can be reconstructed very accurately
based on existing data for $e^+e^-\to 3\pi$, $e^+e^-\to e^+e^-\pi^0$, and the
$\pi^0\to\gamma\gamma$ decay width. We derive a representation that
incorporates all the low-lying singularities of the form factor, matches
correctly onto the asymptotic behavior expected from perturbative QCD, and is
suitable for the evaluation of the $(g-2)_\mu$ loop integral. The resulting
value, $a_\mu^{\pi^0\text{-pole}}=62.6^{+3.0}_{-2.5}\times 10^{-11}$, for the
first time, represents a complete data-driven determination of the pion-pole
contribution with fully controlled uncertainty estimates. In particular, we
show that already improved singly-virtual measurements alone would allow one to
further reduce the uncertainty in $a_\mu^{\pi^0\text{-pole}}$.
