The OPERA experiment is searching for nu(mu) -> nu(tau) oscillations in appearance mode, i.e., via the direct detection of tau leptons in nu(tau) charged-current interactions. The evidence of nu(mu) -> nu(tau) appearance has been previously reported with three nu(tau) candidate events using a sub-sample of data from the 2008-2012 runs. We report here a fourth nu(tau) candidate event, with the tau decaying into a hadron, found after adding the 2012 run events without any muon in the final state to the data sample. Given the number of analyzed events and the low background, nu(mu) -> nu(tau) oscillations are established with a significance of 4.2 sigma.