A search for the Higgs boson with a mass of about $125$ GeV decaying into a pair of $\tau$ leptons is performed with a data sample of proton-proton collisions, corresponding to an integrated luminosity of $\mathcal{L}=20.3$ fb$^{-1}$, collected with the ATLAS detector at the LHC at a centre-of-mass energy of $\sqrt{s}=8$ TeV. Final states in all $\tau$ decay combinations (both hadronic and leptonic) are examined. The observed (expected) deviation from the background-only hypothesis corresponds to a significance of 4.1 (3.2) standard deviations, and the measured signal strength is $\mu = 1.4 ^{+0.5}_{-0.4}$. This is evidence for the existence of $H\rightarrow\tau^+\tau^-$ decays, consistent with the Standard Model expectation for a Higgs boson with $m_H=125$ GeV.

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