We analyse a sample of galaxies with stellar masses greater than 1010M⊙ and with redshifts in the range 0.025 <z <0.05 for which Hi mass measurements are available from the GALEX Arecibo SDSS (Sloan Digital Sky Survey) Survey (GASS) or from the Arecibo Legacy Fast ALFA survey (ALFALFA). At a given value of M*, our sample consists primarily of galaxies that are more Hi-rich than average. We constructed a series of three control samples for comparison with these Hi-rich galaxies: one sample is matched in stellar mass and redshift (CM*), the second sample is matched in stellar mass, NUV -r colour and redshift (CM*, NUV -r), and the third sample is matched in stellar mass, NUV -r colour, stellar surface mass density μ* and redshift. We generated self-consistent seven-band photometry (FUV, NUV, u,g,r,i,z) for all galaxies, and we used this to derive inner colours, outer colours, asymmetry and smoothness parameters. We also used standard spectral energy distribution (SED) fitting techniques to derive inner and outer specific star formation rates (sSFR). As expected, Hi-rich galaxies differ strongly from galaxies of the same stellar mass that are selected without regard to Hi content. The majority of these differences are attributable to the fact that galaxies with more gas are bluer and more actively star forming. In order to identify those galaxy properties that are causally connected with Hicontent, we compare results derived for the Hi sample with those derived for galaxies matched in stellar mass, size and NUV -r colour. The only photometric property that is clearly attributable to increasing Hi content is the colour gradient of the galaxy. Galaxies with larger Hi fractions have bluer, more actively star-forming outer discs compared to the inner part of the galaxy. Hi-rich galaxies also have larger g-band radii compared to i-band radii. Our results are consistent with the 'inside-out' picture of disc galaxy formation, which has commonly served as a basis for semi-analytic models of the formation of discs in the context of cold dark matter cosmologies. The lack of any intrinsic connection between Hi fraction and galaxy asymmetry suggests that gas is accreted smoothly on to the outer disc. © 2010 The Authors Monthly Notices of the Royal Astronomical Society © 2010 RAS.