  We studied the spatial distributions of multiple stellar populations (MPs) in
a sample of 20 globular clusters (GCs) spanning a broad range of dynamical
ages. The differences between first-population (FP) and second-population (SP)
stars were measured by means of the parameter $A^+$, defined as the area
enclosed between their cumulative radial distributions. We provide the first
purely observational evidence of the dynamical path followed by MPs from
initial conditions toward a complete FP-SP spatial mixing. Less dynamically
evolved clusters have SP stars more centrally concentrated than FPs, while in
more dynamically evolved systems the spatial differences between FP and SP
stars decrease and eventually disappear. By means of an appropriate comparison
with a set of numerical simulations, we show that these observational results
are consistent with the evolutionary sequence expected by the long-term
dynamical evolution of clusters forming with an initially more centrally
concentrated SP sub-system. This result is further supported by the evidence of
a trend between $A^+$ and the stage of GC dynamical evolution inferred by the
ratio between the present-day and the initial mass of the cluster.
