  The B-meson distribution amplitude (DA) is defined as the matrix element of a
quark-antiquark bilocal light-cone operator in the heavy-quark effective
theory, corresponding to a long-distance component in the factorization formula
for exclusive B-meson decays. The evolution equation for the B-meson DA is
governed by the cusp anomalous dimension as well as the
Dokshitzer-Gribov-Lipatov-Altarelli-Parisi-type anomalous dimension, and these
anomalous dimensions give the "quasilocal" kernel in the coordinate-space
representation. We show that this evolution equation can be solved analytically
in the coordinate-space, accomplishing the relevant Sudakov resummation at the
next-to-leading logarithmic accuracy. The quasilocal nature leads to a quite
simple form of our solution which determines the B-meson DA with a
quark-antiquark light-cone separation $t$ in terms of the DA at a lower
renormalization scale $\mu$ with smaller interquark separations $zt$ ($z \leq
1$). This formula allows us to present rigorous calculation of the B-meson DA
at the factorization scale $\sim \sqrt{m_b \Lambda_{\rm QCD}}$ for $t$ less
than $\sim 1$ GeV^{-1}, using the recently obtained operator product expansion
of the DA as the input at $\mu \sim 1$ GeV. We also derive the master formula,
which reexpresses the integrals of the DA at $\mu \sim \sqrt{m_b \Lambda_{\rm
QCD}}$ for the factorization formula by the compact integrals of the DA at $\mu
\sim 1$ GeV.
