  We compute NNLO (${\cal O}(\alpha_s^2)$) corrections to the hard-scattering
kernels entering the QCD factorization formula for $B\to V\gamma$ decays, where
$V$ is a light vector meson. We give complete NNLO results for the dipole
operators $Q_7$ and $Q_8$, and partial results for $Q_1$ valid in the
large-$\beta_0$ limit and neglecting the NNLO correction from hard spectator
scattering. Large perturbative logarithms in the hard-scattering kernels are
identified and resummed using soft-collinear effective theory. We use our
results to estimate the branching fractions for $B\to K^*\gamma$ and $B_s\to
\phi\gamma$ decays at NNLO and compare them with the current experimental data.
