© 2017 American Physical Society.van der Waals interactions govern the physics of a plethora of molecular structures. It is well known that the leading term in the distance-based London expansion of the van der Waals energy for atomic and molecular dimers decays as 1/R6, where R is the dimer distance. Using perturbation theory, we find the leading term in the distance-based expansion of the intracule pair density at the interatomic distance. Our results unveil a universal 1/R3 decay, which is less prone to numerical errors than the 1/R6 dependency, and it is confirmed numerically in H2 and He2 molecules. This signature of van der Waals interactions can be directly used in the construction of approximate pair density and energy functionals including vdW corrections.