Results of a search for H -> tau tau decays are presented, based on the full set of proton-proton collision data recorded by the ATLAS experiment at the LHC during 2011 and 2012. The data correspond to integrated luminosities of 4.5 fb(-1) and 20.3 fb(-1) at centre-of-mass energies of root s = 7TeV and root s = 8 TeV respectively. All combinations of leptonic (tau -> l nu(nu) over bar with l = e, mu) and hadronic (tau -> hadrons nu) tau decays are considered. An excess of events over the expected background from other Standard Model processes is found with an observed (expected) significance of 4.5 (3.4) standard deviations. This excess provides evidence for the direct coupling of the recently discovered Higgs boson to fermions. The measured signal strength, normalised to the Standard Model expectation, of mu = 1.43(-0.37)(+0.43) is consistent with the predicted Yukawa coupling strength in the Standard Model.