Results are presented from a search for the rare decays ${B}_{s}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ and ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ in $pp$ collisions at $\sqrt{s}=7$ and 8 TeV, with data samples corresponding to integrated luminosities of 5 and $20\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$, respectively, collected by the CMS experiment at the LHC. An unbinned maximum-likelihood fit to the dimuon invariant mass distribution gives a branching fraction $\mathcal{B}({B}_{s}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})=({3.0}_{\ensuremath{-}0.9}^{+1.0})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$, where the uncertainty includes both statistical and systematic contributions. An excess of ${B}_{s}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ events with respect to background is observed with a significance of 4.3 standard deviations. For the decay ${B}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ an upper limit of $\mathcal{B}({B}^{0}\ensuremath{\rightarrow}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}})<1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}9}$ at the 95% confidence level is determined. Both results are in agreement with the expectations from the standard model.