A search for a standard model Higgs boson decaying into a pair of tau leptons is performed using events recorded by the CMS experiment at the LHC in 2011 and 2012. The dataset corresponds to an integrated luminosity of 4.9 fb(-1) at a centre-of-mass energy of 7 TeV and 19.7 fb(-1) at 8 TeV. Each tau lepton decays hadronically or leptonically to an electron or a muon, leading to six different final states for the tau-lepton pair, all considered in this analysis. An excess of events is observed over the expected background contributions, with a local significance larger than 3 standard deviations for m (H) values between 115 and 130 GeV. The best fit of the observed H -> tau tau signal cross section times branching fraction for m(H) = 125 GeV is 0.78 +/- 0.27 times the standard model expectation. These observations constitute evidence for the 125 GeV Higgs boson decaying to a pair of tau leptons.