  Motivated by a dynamical enhancement of the electromagnetic corrections by a
power of $\Lambda_{\mathrm{QCD}}/m_b$ in $B_{d,s}\, \to\, \mu^+\, \mu^-$ at
next-to-leading order (NLO), we extend the QED factorization effects on the
leptonic $B$ meson decays with light muon leptons to tauonic final states,
$B_{d,s} \, \to\, \tau^+\, \tau^-$, using soft-collinear effective theory
(SCET). This extension is necessary owing to the appearance of the large $\tau$
mass, which will lead to different power counting in SCET and also different
results. We provide a complete NLO electromagnetic corrections to $B_{d,s} \,
\to\, \tau^+\, \tau^-$, which include hard functions and hard-collinear
functions below the bottom quark mass scale $\mu_b$. The power enhanced
electromagnetic effects from hard-collinear contributions on $B_{d,s}\, \to\,
\mu^+\, \mu^-$ discussed before also exist in $B_{d,s} \, \to\, \tau^+\,
\tau^-$. However the logarithm term arising from contributions of
hard-collinear photon and lepton virtualities for $B_{d,s}\, \to\, \tau^+\,
\tau^-$ is not large as it is in muon case due to the hard-collinear scale of
$\tau$ mass, which lead to only approximately $0.04\%$ QED corrections to the
branching fraction of $B_{d,s} \, \to\, \tau^+\, \tau^-$ compared with overall
reduction about $0.5\%$ in $B_{d,s}\, \to\, \mu^+\, \mu^-$.
