The constituent particles of matter can arrange themselves in various ways, giving rise to emergent phenomena that can be surprisingly rich and often cannot be understood by studying only the individual constituents. Discovering and understanding the emergence of such phenomena in quantum materials-especially those in which multiple degrees of freedom or energy scales are delicately balanced-is of fundamental interest to condensed-matter research1,2. Here we report on the surprising observation of emergent ferroelectricity in graphene-based moiré heterostructures. Ferroelectric materials show electrically switchable electric dipoles, which are usually formed by spatial separation between the average centres of positive and negative charge within the unit cell. On this basis, it is difficult to imagine graphene-a material composed of only carbon atoms-exhibiting ferroelectricity3. However, in this work we realize switchable ferroelectricity in Bernal-stacked bilayer graphene sandwiched between two hexagonal boron nitride layers. By introducing a moiré superlattice potential (via aligning bilayer graphene with the top and/or bottom boron nitride crystals), we observe prominent and robust hysteretic behaviour of the graphene resistance with an externally applied out-of-plane displacement field. Our systematic transport measurements reveal a rich and striking response as a function of displacement field and electron filling, and beyond the framework of conventional ferroelectrics. We further directly probe the ferroelectric polarization through a non-local monolayer graphene sensor. Our results suggest an unconventional, odd-parity electronic ordering in the bilayer graphene/boron nitride moiré system. This emergent moiré ferroelectricity may enable ultrafast, programmable and atomically thin carbon-based memory devices.