Taking advantage of ~4700 deg^2^ optical coverage of the Southern sky offered by the VST ATLAS survey, we construct a new catalogue of photometrically selected galaxy groups and clusters using the orca cluster detection algorithm. The catalogue contains ~22 000 detections with N200 > 10 and ~9000 with N200 > 20. We estimate the photometric redshifts of the clusters using machine learning and find the redshift distribution of the sample to extend to z ~ 0.7, peaking at z ~ 0.25. We calibrate the ATLAS cluster mass-richness scaling relation using masses from the MCXC, Planck, ACT DR5, and SDSS redMaPPer cluster samples. We estimate the ATLAS sample to be > 95 per cent complete and > 85 per cent pure at z < 0.35 and in the M_200m_ > 1 * 10^14^ h^-1^ M_{Sun}_ mass range. At z < 0.35, we also find the ATLAS sample to be more complete than redMaPPer, recovering a ~ 40 per cent higher fraction of Abell clusters. This higher sample completeness places the amplitude of the z < 0.35 ATLAS cluster mass function closer to the predictions of a LCDM model with parameters based on the Planck CMB analyses, compared to the mass functions of the other cluster samples. However, strong tensions between the observed ATLAS mass functions and models remain. We shall present a detailed cosmological analysis of the ATLAS cluster mass functions in paper II. In the future, optical counterparts to X-ray-detected eROSITA clusters can be identified using the ATLAS sample. The catalogue is also well suited for auxiliary spectroscopic target selection in 4MOST. The ATLAS cluster catalogue is publicly available at http://astro.dur.ac.uk/cosmology/vstatlas/cluster_catalogue/.