In this work, the evolution of the optical properties of nanoscale spatially indirect excitons as a function of the size, shape, and composition of the heteronanostructure is investigated, using colloidal CdTe/CdSe heteronanocrystals (2.6 nm diameter CdTe core and increasing CdSe volume fraction) as a model system. Emphasis is given to quantitative aspects such as the absorption cross section of the lowest-energy exciton transition (μSS), Stokes shift, linewidths, and the exciton radiative lifetime. The hole wave function remains confined to the CdTe core while the electron wave function is initially delocalized over the whole heteronanocrystal (type-I1/2 regime), and gradually localizes in the CdSe segment as the growth proceeds, until the spatially indirect exciton transition becomes the lowest-energy transition (type-II regime). This results in a progressive shift of the optical transitions to lower energies, accompanied by a decrease in the oscillator strengths at emission energies and an increase in the exciton radiative lifetimes. The onset of the type-II regime is characterized by the loss of structure of the lowest-energy absorption band, accompanied by a simultaneous increase in the Stokes shift values and transition linewidths. This can be understood by considering the dispersion of the hole and electron states in k space. The μSS values decrease rapidly in the type-I1/2 regime but only slightly in the type-II regime. This shows that the indirect exciton formation leads primarily to redistribution of the oscillator strength of the lowest-energy transition over a wider frequency range. The total absorption cross section per ion-pair unit (i.e., integrated over all the exciton transitions) remains essentially constant during the heteronanocrystal growth, demonstrating that μSS is redistributed from higher-energy transitions of both the CdTe and the CdSe segments, in response to the reduction in the electron-hole wave-function overlap. Two radiative decay rates are observed and ascribed to exciton states with different degrees of localization of the electron wave function (an upper state with a faster decay rate and a lower state with a slower decay rate). The results presented here provide fundamental insights into nanoscale spatially indirect exciton transitions, highlighting the crucial role of a number of parameters (viz., electron-hole spatial correlation, exciton dispersion and exciton degeneracy, shape effects, and electronic coupling).