Multiferroics are compounds in which at least two ferroic orders coexist, typically ferroelectricity and some form of magnetism. While magnetic order can arise in both insulating and metallic compounds, ferroelectricity is in principle only allowed in insulators, although ferroelectric metals have been proposed and several two-dimensional systems have been reported to behave in this way. However, their combination with and coupling to magnetic order have not been realized thus far. Here we show the coexistence of ferroelectricity and magnetism in an oxide-based two-dimensional electron gas. We report a modulation of the Ti-O polar displacements depending on the ferroelectric polarization direction, and a voltage-induced hysteresis of the sheet resistance that is reminiscent of the ferroelectric polarization loop. The transport properties of the electron gas display an anomalous Hall effect and magnetoresistance that can both be modulated and cycled by switching the remanent polarization, demonstrating a magnetoelectric coupling. Our findings provide new opportunities in quantum matter that stem from the interplay between ferroelectricity, ferromagnetism, metallicity and Rashba spin-orbit coupling.