This paper presents a search for exotic decays of the Higgs boson into a pair of new pseudoscalar particles, H → aa, where one pseudoscalar decays into a b-quark pair and the other decays into a τ-lepton pair, in the mass range 12 ≤ m_a ≤ 60 GeV. The analysis uses pp collision data at √s = 13 TeV collected with the ATLAS detector at the LHC, corresponding to an integrated luminosity of 140 fb^-1. No significant excess above the Standard Model ( SM) prediction is observed. Assuming the SM Higgs boson production cross section, the search sets upper limits at 95% confidence level on the branching ratio of Higgs bosons decaying into bb<over bar>τ⁺τ^-, B(H → aa → bb<over bar>τ⁺τ^-), between 2.2% and 3.9% depending on the pseudoscalar mass.