This thesis presents the results of a search for Standard Model Higgs bosons decaying to tau lepton pairs, where both tau leptons decay hadronically. The search is performed using the proton-proton collision data collected in 2012 by the ATLAS detector at the Large Hadron Collider at CERN. The search is complicated by a significant source of background events from non-resonant multijet processes and by di-tau events from Z boson decays that share similar features with the Higgs signal. The multijet background is estimated from a control region in data, and the Z→ττ background is estimated from Z→μμ events in data where the muons are replaced by simulated tau leptons. Other minor backgrounds are estimated from simulation. A multivariate analysis using boosted decision trees is optimized to search for Higgs events produced via gluon-gluon fusion and vector boson fusion at a Higgs mass of 125 GeV. A cut-based analysis is also developed and presented in support of the multivariate analysis. An excess of events over the expected background is observed with a statistical significance of 2.9 standard deviations. When combined with excesses observed by searches in the fully leptonic and semi-leptonic final states, the statistical significance reaches 4.5 standard deviations. The combined excess is compatible with and provides direct evidence for the coupling of the recently discovered Higgs boson to fermions.