We use Hubble Space Telescope (HST) to reach the end of the white dwarf (WD) cooling sequence (CS) in the solar-metallicity open cluster NGC 6819. Our photometry and completeness tests show a sharp drop in the number of WDs along the CS at magnitudes fainter than mF606W = 26.050+/- 0.075. This implies an age of 2.25+/-0.20 Gyr, consistent with the age of 2.25+/-0.30 Gyr obtained from fits to the main-sequence turn-off. The use of different WD cooling models and initial-final-mass relations have a minor impact the WD age estimate, at the level of ~0.1 Gyr. As an important by-product of this investigation we also release, in electronic format, both the catalogue of all the detected sources and the atlases of the region (in two filters). Indeed, this patch of sky studied by HST (of size ~70 arcmin sq.) is entirely within the main Kepler-mission field, so the high-resolution images and deep catalogues will be particularly useful. ; Comment: 11 pages, 7 figures (4 at low resolution). Accepted for publication in MNRAS on January 12, 2015