Context. Red supergiants are the evolved descendants of massive stars with initial masses between 7 and 40 M⊙. Their brightness makes them easily detectable in the near infrared, making them useful probes of star formation that occurred several tens of Myr ago. Aims: We investigate the past star formation history of Cygnus OB2, the nearest very massive OB association, using red supergiants as a probe. Our aim is to confirm the evidence, found by previous studies, that star formation in the Cygnus OB2 region started long before the latest burst that gave rise to the dense aggregate of early O-type stars that dominate the appearance of the association at present. Methods: Near-infrared star counts in the Cygnus region reveal moderate evidence for a peak in the areal density of bright, reddened stars approximately coincident with Cygnus OB2. A total of 11 sources are found within a circle of 1° radius centered on the association, of which 4 are non-supergiants based on existing observations. Near-infrared spectroscopy is presented of the remaining seven candidates, including four that have been already classified as M supergiants in the literature. Results: We confirm the presence of seven red supergiants in the region and argue that they are probably physically associated with Cygnus OB2. Their location is roughly coincident with that of the older population identified by previous studies, supporting the scenario in which the main star formation activity in the association has been shifting toward higher Galactic longitudes with time. Their luminosities are compared with the predictions of evolutionary tracks with and without rotation to estimate the mass of their progenitors and ages. In this way, we confirm that massive star formation was already taking place in the area of Cygnus OB2 over 20 Myr ago, and we estimate that the star formation rate in the latest 6 Myr represents a six-fold increase over the massive star formation rate at the time when the progenitors of the current red supergiants were formed. Conclusions: The Cygnus OB2 association has a history of star formation extending into the past for at least about 20 Myr, probably dovetailing with the general history of star formation in the region that gave rise to other associations like the neighboring Cygnus OB9. The sustained massive star formation history also argues for a long lifetime of the giant molecular complex from which Cygnus OB2 formed, whose remnants constitute the present-day Cygnus X complex.