Quantitative explanation for the odd–even effect on fragment angular momenta in the low-energy fission of actinides have been provided by taking into account the single particle spin of the odd proton at the fragment's scission point deformation in the case of odd-𝑍 fragments along with the contribution from the population of angular momentum bearing collective vibrations of the fissioning nucleus at scission point. The calculated fragment angular momenta have been found to be in very good agreement with the experimental data for fragments in the mass number region of 130–140. The odd–even effect observed in the fragment angular momenta in the low-energy fission of actinides has been explained quantitatively for the first time.