A measurement of total and fiducial inclusive $W$ and $\mathrm{Z}$ boson production cross sections in $pp$ collisions at $\sqrt{s}=8\text{ }\text{ }\mathrm{TeV}$ is presented. Electron and muon final states are analyzed in a data sample collected with the CMS detector corresponding to an integrated luminosity of $18.2\ifmmode\pm\else\textpm\fi{}0.5\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$. The measured total inclusive cross sections times branching fractions are $\ensuremath{\sigma}(pp\ensuremath{\rightarrow}WX)\ifmmode\times\else\texttimes\fi{}\mathcal{B}(W\ensuremath{\rightarrow}\ensuremath{\ell}\ensuremath{\nu})=12.21\ifmmode\pm\else\textpm\fi{}0.03(\text{stat})\ifmmode\pm\else\textpm\fi{}0.24(\text{syst})\ifmmode\pm\else\textpm\fi{}0.32(\mathrm{lum})\text{ }\text{ }\mathrm{nb}$ and $\ensuremath{\sigma}(pp\ensuremath{\rightarrow}\mathrm{Z}X)\ifmmode\times\else\texttimes\fi{}\mathcal{B}(\mathrm{Z}\ensuremath{\rightarrow}{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}})=1.15\ifmmode\pm\else\textpm\fi{}0.01(\text{stat})\ifmmode\pm\else\textpm\fi{}0.02(\text{syst})\ifmmode\pm\else\textpm\fi{}0.03(\mathrm{lum})\text{ }\text{ }\mathrm{nb}$ for the dilepton mass in the range of 60---120 GeV. The measured values agree with next-to-next-to-leading-order QCD cross section calculations. Ratios of cross sections are reported with a precision of 2%. This is the first measurement of inclusive $W$ and $\mathrm{Z}$ boson production in proton-proton collisions at $\sqrt{s}=8\text{ }\text{ }\mathrm{TeV}$.