Finding the basic mechanism governing the surface history of asteroids of various shapes is essential for understanding their origin and evolution. In particular, the asteroids (162173) Ryugu1 and (101955) Bennu2 currently being visited by Hayabusa2 and OSIRIS-REx appear to be top shaped. This distinctive shape, characterized by a raised equatorial bulge, is shared by other similarly sized asteroids, including Didymos A3, 2008 EV54 and 1999 KW4 Alpha5. However, the possibly common formation mechanism that causes the top-like shape is still under debate. One clue may lie in the boulders on their surfaces. The distribution of these boulders, which was precisely measured in unprecedented detail by the two spacecraft1,2, constitutes a record of the geological evolution of the surface regolith since the origin of these asteroids. Here, we show that during the regolith migration driven by Yarkovsky-O'Keefe-Radzievskii-Paddack spin-up6-9 the surface boulders coevolve with the underlying regolith and exhibit diverse dynamical behaviours: they can remain undisturbed, sink into the regolith layer and become tilted, or be totally buried by the downslope deposition, depending on their latitudes. The predominant geological features commonly observed on top-shaped asteroids, including the boulder-rich region near the pole1,10, the deficiency of large boulders in the equatorial area10,11 and partially buried, oblique boulders exposed on the regolith surface12,13, are commensurate with this coevolution scenario. The surface regolith migration thus is the prevalent mechanism for the formation history of the top-shaped asteroids with stiffer cores.