The majority of massive stars ($>8$ $rm{M_{odot}}$) in OB associations are found in close binary systems. Nonetheless, the formation mechanism of these close massive binaries is not understood yet. Using literature data, we measured the radial-velocity dispersion ($sigma_mathrm{RV}$) as a proxy for the close binary fraction in ten OB associations in the Galaxy and the Large Magellanic Cloud, spanning an age range from 1 to 6 Myrs. We find a positive trend of this dispersion with the clusters age, which is consistent with binary hardening. Assuming a universal binary fraction of $f_mathrm{bin}$ = 0.7, we converted the $sigma_mathrm{RV}$ behavior to an evolution of the minimum orbital period $P_mathrm{cutoff}$ from $sim$9.5 years at 1 Myr to $sim$1.4 days for the oldest clusters in our sample at $sim$6 Myr. Our results suggest that binaries are formed at larger separations, and they harden in around 1 to 2 Myrs to produce the period distribution observed in few million year-old OB binaries. Such an inward migration may either be driven by an interaction with a remnant accretion disk or with other young stellar objects present in the system. Our findings constitute the first empirical evidence in favor of migration as a scenario for the formation of massive close binaries.
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