The majority of massive stars ( > 8 M (cid:12) ) 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 ( σ 1D ) 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 6Myr. We find a positive trend of this dispersion with the cluster’s age, which is consistent with binary hardening. Assuming a universal binary fraction of f bin = 0.7, we converted the σ 1D behavior to an evolution of the minimum orbital period P cuto ff from ∼ 9.5years at 1Myr to ∼ 1.4days for the oldest clusters in our sample at ∼ 6Myr. Our results suggest that binaries are formed at larger separations, and they harden in around 1 to 2Myr 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.