A search for the decay of the Standard Model Higgs boson into a bb¯ pair when produced in association with a W or Z boson is performed with the ATLAS detector. The data, corresponding to an integrated luminosity of 79.8fb−1 were collected in proton–proton collisions during Run 2 of the Large Hadron Collider at a centre-of-mass energy of 13TeV . For a Higgs boson mass of 125GeV , an excess of events over the expected background from other Standard Model processes is found with an observed (expected) significance of 4.9 (4.3) standard deviations. A combination with the results from other searches in Run 1 and in Run 2 for the Higgs boson in the bb¯ decay mode is performed, which yields an observed (expected) significance of 5.4 (5.5) standard deviations, thus providing direct observation of the Higgs boson decay into b -quarks. The ratio of the measured event yield for a Higgs boson decaying into bb¯ to the Standard Model expectation is 1.01±0.12(stat.)−0.15+0.16(syst.) . Additionally, a combination of Run 2 results searching for the Higgs boson produced in association with a vector boson yields an observed (expected) significance of 5.3 (4.8) standard deviations.