Results are reported for the $$ {\mathrm{B}}_{\mathrm{s}}^0 $$ μ μ branching fraction and effective lifetime and from a search for the decay B μ μ . The analysis uses a data sample of proton-proton collisions accumulated by the CMS experiment in 2011, 2012, and 2016, with center-of-mass energies (integrated luminosities) of 7 TeV (5 fb 1 ), 8 TeV (20 fb 1 ), and 13 TeV (36 fb 1 ). The branching fractions are determined by measuring event yields relative to B J ψK decays (with J ψ μ μ ), which results in the reduction of many of the systematic uncertainties. The decay $$ {\mathrm{B}}_{\mathrm{s}}^0 $$ μ μ is observed with a significance of 5.6 standard deviations. The branching fraction is measured to be $$ \mathrm{\mathcal{B}}\left({\mathrm{B}}_{\mathrm{s}}^0\to {\upmu}^{+}{\upmu}^{-}\right)=\left[2.9\pm 0.7\left(\exp \right)\pm 0.2\left(\mathrm{frag}\right)\right]\times {10}^{-9} $$ , where the first uncertainty combines the experimental statistical and systematic contributions, and the second is due to the uncertainty in the ratio of the $$ {\mathrm{B}}_{\mathrm{s}}^0 $$ and the B fragmentation functions. No significant excess is observed for the decay B μ μ , and an upper limit of ℬ(B → μ μ ) < 3.6 × 10 is obtained at 95% confidence level. The $$ {\mathrm{B}}_{\mathrm{s}}^0 $$ μ+μ effective lifetime is measured to be $$ {\tau}_{\upmu^{+}{\upmu}^{-}}={1.70}_{-0.44}^{+0.61} $$ ps. These results are consistent with standard model predictions.