We present the deepest near-infrared ( ZJK _ { s } ) photometry yet obtained of the Sagittarius dwarf spheroidal ( Sgr dSph ) , using VISTA to survey 11 square degrees centred on its core . We list locations and ZJK _ { s } -band magnitudes for over 2.9 million sources in the field . We discuss the isolation of the Sgr dSph from the foreground and Galactic Bulge populations , identify the Sgr dSph ’ s horizontal branch in the near-infrared for the first time , and map the density of the galaxy ’ s stars . We present isochrones for the Sgr dSph and Bulge populations . These are consistent with the previously-reported properties of the Sgr dSph core : namely that it is dominated by a population between [ Fe/H ] \approx –1 dex and solar , with a significant [ \alpha /Fe ] versus [ Fe/H ] gradient . While strong contamination from the Galactic Bulge prevents accurate measurement of the ( Galactic ) north side of the Sgr dSph , the dwarf galaxy can be well-approximated by a roughly ovaloid projection of characteristic size 4 ^ { \circ } \times 2 ^ { \circ } , beyond which the projected stellar density is less than half that of the region surrounding the core . The galaxy ’ s major axis is perpendicular to the Galactic Plane , as in previous studies . We find slight evidence to confirm a metallicity gradient in the Sgr dSph and use isochrones to fit a distance of 24.3 \pm 2.3 kpc . We were unable to fully constrain the metallicity distribution of the Sgr dSph due to the Bulge contamination and strong correlation of [ \alpha /Fe ] with metallicity , however we find that metal-poor stars ( [ Fe/H ] < \sim –1 ) make up < \sim 29 per cent of the Sgr dSph ’ s upper-RGB population . The Bulge population is best fit by a younger population with [ Fe/H ] \approx 0 and [ \alpha /Fe ] \approx 0 or slightly higher . We find no evidence for a split , peanut- or X-shaped Bulge population in this line of sight ( l = 5.6 ^ { \circ } \pm \sim 1 ^ { \circ } , b = -14.1 ^ { \circ } \pm \sim 3 ^ { \circ } ) .