Properties of the Higgs boson with mass near 125 GeV are measured in proton-proton collisions with the CMS experiment at the LHC. Comprehensive sets of production and decay measurements are combined. The decay channels include gamma gamma, ZZ, WW, tau tau, bb, and mu mu pairs. The data samples were collected in 2011 and 2012 and correspond to integrated luminosities of up to 5.1 fb(-1) at 7 TeV and up to 19.7 fb(-1) at 8 TeV. From the high-resolution gamma gamma and ZZ channels, the mass of the Higgs boson is determined to be 125.02(-0.27)(+0.26) (stat)(-0.15)(+0.14) (syst) GeV. For this mass value, the event yields obtained in the different analyses tagging specific decay channels and production mechanisms are consistent with those expected for the standard model Higgs boson. The combined best-fit signal relative to the standard model expectation is 1.00 +/- 0.09 (stat)(-0.07)(+0.08) (theo) +/- 0.07 (syst) at the measured mass. The couplings of the Higgs boson are probed for deviations in magnitude from the standard model predictions in multiple ways, including searches for invisible and undetected decays. No significant deviations are found.