The perpendicular exchange bias field, H(EB), of the magnetoelectric heterostructure Cr2O3(111)/(Co/Pt)(3) changes sign after field cooling to below the Néel temperature of Cr2O3 in either parallel or antiparallel axial magnetic and electric freezing fields. The switching of H(EB) is explained by magnetoelectrically induced antiferromagnetic single domains which extend to the interface, where the direction of their end spins controls the sign of H(EB). Novel applications in magnetoelectronic devices seem possible.