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The Low-Frequency Array (LOFAR) Long-Baseline Calibrator Survey (LBCS) wasconducted between 2014 and 2019 in order to obtain a set of suitablecalibrators for the LOFAR array. In this paper we present the complete survey,building on the preliminary analysis published in 2016 which coveredapproximately half the survey area. The final catalogue consists of 30006observations of 24713 sources in the northern sky, selected for a combinationof high low-frequency radio flux density and flat spectral index using existingsurveys (WENSS, NVSS, VLSS, and MSSS). Approximately one calibrator per squaredegree, suitable for calibration of $\geq$ 200 km baselines is identified bythe detection of compact flux density, for declinations north of 30 degrees andaway from the Galactic plane, with a considerably lower density south of thispoint due to relative difficulty in selecting flat-spectrum candidate sourcesin this area of the sky. Use of the VLBA calibrator list, together withstatistical arguments by comparison with flux densities from lower-resolutioncatalogues, allow us to establish a rough flux density scale for the LBCSobservations, so that LBCS statistics can be used to estimate compact fluxdensities on scales between 300 mas and 2 arcsec, for sources observed in thesurvey. The LBCS can be used to assess the structures of point sources inlower-resolution surveys, with significant reductions in the degree ofcoherence in these sources on scales between 2 arcsec and 300 mas. The LBCSsurvey sources show a greater incidence of compact flux density in quasars thanin radio galaxies, consistent with unified schemes of radio sources. Comparisonwith samples of sources from interplanetary scintillation (IPS) studies withthe Murchison Widefield Array (MWA) shows consistent patterns of detection ofcompact structure in sources observed both interferometrically with LOFAR andusing IPS.

Sub-arcsecond imaging with the International LOFAR Telescope: II. Completion of the LOFAR Long-Baseline Calibrator Survey