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The luminosity determination for the ATLAS detector at the LHC during Run 2 is presented, with collisions at TeV. The absolute luminosity scale is determined using van der Meer beam separation scans during dedicated running periods in each year, and extrapolated to the physics data-taking regime using complementary measurements from several luminosity-sensitive detectors. The total uncertainties in the integrated luminosities for each individual year of data-taking range from 0.9% to 1.1%, and are partially correlated between years. After standard data-quality selections, the full Run 2 data sample corresponds to an integrated luminosity of fb, i.e. an uncertainty of 0.83%. A dedicated sample of low-pileup data recorded in 2017-18 for precision Standard Model physics measurements is analysed separately, and has an integrated luminosity of pb.