We present the first survey of resolved stellar populations in the remote outer halo of our nearest giant elliptical (gE), Centaurus A (D = 3.8 Mpc). Using the VIsible Multi Object Spectrograph (VIMOS)/Very Large Telescope (VLT) optical camera, we obtained deep photometry for four fields along the major and minor axes at projected elliptical radii of similar to 30-85 kpc (corresponding to similar to 5-14R(eff)). We use resolved star counts to map the spatial and colour distribution of red giant branch (RGB) stars down to similar to 2 mag below the RGB tip. We detect an extended halo out to the furthermost elliptical radius probed (similar to 85 kpc or similar to 14R(eff)), demonstrating the vast extent of this system. We detect a localized substructure in these parts, visible in both (old) RGB and (intermediate-age) luminous asymptotic giant branch stars, and there is some evidence that the outer halo becomes more elliptical and has a shallower surface brightness profile. We derive photometric metallicity distribution functions for halo RGB stars and find relatively high median metallicity values (<Fe/H similar to -0.9 to -1.0 dex) that change very little with radius over the extent of our survey. Radial metallicity gradients are measured to be approximate to -0.002-0.004 dex kpc(-1), and the fraction of metal-poor stars (defined as [Fe/H] < -1.0) is approximate to 40-50 per cent at all radii. We discuss these findings in the context of galaxy formation models for the buildup of gE haloes.