Milky Way demographics with the VVV survey: IV. PSF photometry from almost one billion stars in the Galactic bulge and adjacent southern disk

Context. The inner regions of the Galaxy are severely affected by extinction, which limits our capability to study the stellar populations present there. The Vista Variables in the Vía Láctea (VVV) ESO Public Survey has observed this zone at near-infrared wavelengths where reddening is highly diminished. Aims. By exploiting the high resolution and wide field-of-view of the VVV images we aim to produce a deep, homogeneous, and highly complete database of sources that cover the innermost regions of our Galaxy. Methods. To better deal with the high crowding in the surveyed areas, we have used point spread function (PSF)-fitting techniques to obtain a new photometry of the VVV images, in the ZY JHK_s near-infrared filters available. Results. Our final catalogs contain close to one billion sources, with precise photometry in up to five near-infrared filters, and they are already being used to provide an unprecedented view of the inner Galactic stellar populations. We make these catalogs publicly available to the community. Our catalogs allow us to build the VVV giga-CMD, a series of color-magnitude diagrams of the inner regions of the Milky Way presented as supplementary videos. We provide a qualitative analysis of some representative CMDs of the inner regions of the Galaxy, and briefly mention some of the studies we have developed with this new dataset so far.