One of the central challenges in realizing multiferroics-based magnetoelectric memories is to switch perpendicular magnetic anisotropy (PMA) with a control voltage. In this study, we demonstrate electrical flipping of magnetization between the out-of-plane and the in-plane directions in (Co/Pt)3/(011) Pb(Mg1/3Nb2/3)O3-PbTiO3 multiferroic heterostructures through a voltage-controllable spin reorientation transition (SRT). The SRT onset temperature can be dramatically suppressed at least 200 K by applying an electric field, accompanied by a giant electric-field-induced effective magnetic anisotropy field ($Δ$Heff) up to 1100 Oe at 100 K. In comparison with conventional strain-mediated magnetoelastic coupling that provides a $Δ$Heff of only 110 Oe, that enormous effective field is mainly related to the interface effect of electric field modification of spin-orbit coupling from Co/Pt interfacial hybridization via strain. Moreover, electric field control of SRT is also achieved at room temperature, resulting in a $Δ$Heff of nearly 550 Oe. In addition, ferroelastically nonvolatile switching of PMA has been demonstrated in this system. E-field control of PMA and SRT in multiferroic heterostructures not only provides a platform to study strain effect and interfacial effect on magnetic anisotropy of the ultrathin ferromagnetic films but also enables the realization of power efficient PMA magnetoelectric and spintronic devices.