Magnetization dynamics induced by spin–orbit torques in a heavy-metal/ferromagnet can potentially be used to design low-power spintronics and logic devices. Recent computations have suggested that a strain-mediated spin–orbit torque (SOT) switching in magnetoelectric (ME) heterostructures is fast, energy-efficient, and permits a deterministic 180° magnetization switching. However, its experimental realization has remained elusive. Here, the coexistence of the strain-mediated ME coupling and the SOT in a CoFeB/Pt/ferroelectric hybrid structure is shown experimentally. The voltage-induced strain only slightly modifies the efficiency of SOT generation, but it gives rise to an effective magnetic anisotropy and rotates the magnetic easy axis which eliminates the incubation delay in current-induced magnetization switching. The phase field simulations show that the electric-field-induced effective magnetic anisotropy field can reduce the switching time approximately by a factor of three for SOT in-plane magnetization switching. It is anticipated that such strain-mediated ME-SOT hybrid structures may enable field-free, ultrafast magnetization switching.