The properties of a Higgs boson candidate are measured in the $H\ensuremath{\rightarrow}ZZ\ensuremath{\rightarrow}4\ensuremath{\ell}$ decay channel, with $\ensuremath{\ell}=e$, $\ensuremath{\mu}$, using data from $pp$ collisions corresponding to an integrated luminosity of $5.1\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ at the center-of-mass energy of $\sqrt{s}=7\text{ }\text{ }\mathrm{TeV}$ and $19.7\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}\text{1}}$ at $\sqrt{s}=8\text{ }\text{ }\mathrm{TeV}$, recorded with the CMS detector at the LHC. The new boson is observed as a narrow resonance with a local significance of 6.8 standard deviations, a measured mass of $125.6\ifmmode\pm\else\textpm\fi{}0.4(\text{stat})\ifmmode\pm\else\textpm\fi{}0.2(\text{syst})\text{ }\text{ }\mathrm{GeV}$, and a total width $\ensuremath{\le}3.4\text{ }\text{ }\mathrm{GeV}$ at the 95% confidence level. The production cross section of the new boson times its branching fraction to four leptons is measured to be ${0.93}_{\ensuremath{-}0.23}^{+0.26}{(\text{stat})}_{\ensuremath{-}0.09}^{+0.13}(\text{syst})$ times that predicted by the standard model. Its spin-parity properties are found to be consistent with the expectations for the standard-model Higgs boson. The hypotheses of a pseudoscalar and all tested spin-1 boson hypotheses are excluded at the 99% confidence level or higher. All tested spin-2 boson hypotheses are excluded at the 95% confidence level or higher.