We present F850LP − F160W colour gradients for 11 early-type galaxies (ETGs) at 1.0 < zspec < 1.9 selected from the GOODS-South field. Significant negative F850LP − F160W colour gradients (core redder than the outskirts) have been detected in ∼70 per cent of our sample within the effective radius Re, the remaining 30 per cent having a flat colour profile consistent with a null gradient. Extending the analysis to R > Re, enclosing the whole galaxy, we have found that the fraction of high-z ETGs with negative F850LP − F160W colour gradients rises up to 100 per cent. For each galaxy, we investigate the origin of the radial colour variation with an innovative technique based on the matching of both the spatially resolved colour and the global spectral energy distribution (SED) to predictions of composite stellar population models. In fact, we find that the age of the stellar populations is the only parameter whose radial variation alone can fully account for the observed colour gradients and global SEDs for six ETGs in our sample, without the need of radial variation of any other stellar population property. For four out of these six ETGs, a pure metallicity variation can also reproduce the detected colour gradients. None the less, a minor contribution to the observed colour gradients from the radial variation of star formation time-scale, abundance of low- to high-mass stars and dust cannot be completely ruled out. For the rest of the sample, our analysis suggests a more complex scenario whereby more properties of the stellar populations need to simultaneously vary, likely with comparable weights, to generate the observed colour gradients and global SEDs. Our results show that, despite the young mean age of our galaxies (<3–
4 Gyr), they already exhibit significant differences among their stellar content. We have discussed our results within the framework of the widest accepted scenarios of galaxy formation and conclude that none of them can satisfactorily account for the observed distribution of colour gradients and for the spatially resolved content of high-z ETGs. Our results suggest that the distribution of colour gradients may be due to different initial conditions in the formation mechanisms of ETGs.