The radial density profiles of stellar galaxy discs can be well approximated as an exponential. Compared to this canonical form, however, the profiles in the majority of disc galaxies show downward or upward breaks at large radii. Currently, there is no coherent explanation in a galaxy formation context of the radial profile per se, along with the two types of profile breaks. Using a set of controlled hydrodynamic simulations of disc galaxy formation, we find a correlation between the host halos initial angular momentum and the resulting radial profile of the stellar disc: galaxies that live in haloes with a low spin parameter {lambda} <~ 0.03 show an up-bending break in their disc density profiles, while galaxies in haloes of higher angular momentum show a down-bending break. We find that the case of pure exponential profiles ({lambda} ~ 0.035) coincides with the peak of the spin parameter distribution from cosmological simulations. Our simulations not only imply an explanation of the observed behaviours, but also suggest that the physical origin of this effect is related to the amount of radial redistribution of stellar mass, which is anti-correlated with {lambda}.