Electroweak Corrections to B_{s,d} to ell^+ ell^-

We calculate the full two-loop electroweak matching corrections to the operator governing the decay B_q --> l^+ l^- in the Standard Model. Their inclusion removes an electroweak scheme and scale uncertainty of about 7% of the branching ratio. Using different renormalization schemes of the involved electroweak parameters, we estimate residual perturbative electroweak and QED uncertainties to be less than 1% at the level of the branching ratio.