A magnon is a collective excitation of the spin structure in a magnetic insulator and can transmit spin angular momentum with negligible dissipation. This quantum of a spin wave has always been manipulated through magnetic dipoles (that is, by breaking time-reversal symmetry). Here we report the experimental observation of chiral spin transport in multiferroic BiFeO₃ and its control by reversing the ferroelectric polarization (that is, by breaking spatial inversion symmetry). The ferroelectrically controlled magnons show up to 18% modulation at room temperature. The spin torque that the magnons in BiFeO₃ carry can be used to efficiently switch the magnetization of adjacent magnets, with a spin–torque efficiency comparable to the spin Hall effect in heavy metals. Utilizing such controllable magnon generation and transmission in BiFeO₃, an all-oxide, energy-scalable logic is demonstrated composed of spin–orbit injection, detection and magnetoelectric control. Our observations open a new chapter of multiferroic magnons and pave another path towards low-dissipation nanoelectronics.