The technological appeal of multiferroics is the ability to control magnetism with electric field(1-3). For devices to be useful, such control must be achieved at room temperature. The only single-phase multiferroic material exhibiting unambiguous magnetoelectric coupling at room temperature is BiFeO3 (refs 4 and 5). Its weak ferromagnetism arises from the canting of the antiferromagnetically aligned spins by the Dzyaloshinskii-Moriya (DM) interaction(6-9). Prior theory considered the symmetry of the thermodynamic ground state and concluded that direct 180-degree switching of the DM vector by the ferroelectric polarization was forbidden(10,11). Instead, we examined the kinetics of the switching process, something not considered previously in theoretical work(10-12). Here we show a deterministic reversal of the DM vector and canted moment using an electric field at room temperature. First-principles calculations reveal that the switching kinetics favours a two-step switching process. In each step the DM vector and polarization are coupled and 180-degree deterministic switching of magnetization hence becomes possible, in agreement with experimental observation. We exploit this switching to demonstrate energy-efficient control of a spin-valve device at room temperature. The energy per unit area required is approximately an order of magnitude less than that needed for spin-transfer torque switching(13,14). Given that the DM interaction is fundamental to singlephase multiferroics and magnetoelectrics(3,9), our results suggest ways to engineer magnetoelectric switching and tailor technologically pertinent functionality for nanometre-scale, low-energy-consumption, non-volatile magnetoelectronics.