The luminosity determination for the ATLAS detector at the LHC during Run 2 is presented, with pp collisions at a centre-of-mass energy $\sqrt{s}=13$ 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 luminosity 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 pp data sample corresponds to an integrated luminosity of $140.1\pm 1.2$ $\hbox {fb}^{-1}$, i.e. an uncertainty of 0.83%. A dedicated sample of low-pileup data recorded in 2017–2018 for precision Standard Model physics measurements is analysed separately, and has an integrated luminosity of $338.1\pm 3.1$ $\hbox {pb}^{-1}$.