Medipix and Timepix devices, installed in the ATLAS cavern, have provided valuable complementary luminosity information. Results are presented from measurements with the Timepix3 (TPX3) detectors. In contrast with previously employed frame-based data acquisition, the TPX3 detector remains active continuously, sending information on the pixel hits as they occur. The hit- and cluster-counting methods were used for the luminosity determination of the Large Hadron Collider (LHC) proton–proton collisions. The LHC luminosity versus time is determined using these two methods and fits to a simple model, which incorporates luminosity reduction from the single bunch and beam–beam interactions. The precision of the luminosity determination could be improved by counting the number of clusters, instead of just pixel hits. The internal precision and long-term stability of the TPX3 luminosity measurements are below 0.5%. TPX3, owing to its 1.56-ns time-tagging, is able to resolve the time structure of the luminosity due to the collisions of the individual proton bunches when integrated over an LHC fill.