Neuromorphic photonic processors are redefining the boundaries of classical computing by enabling high-speed multidimensional information processing within the memory. Memristors, the backbone of neuromorphic processors, retain their state after programming without static power consumption. Among them, electro-optic memristors are of great interest, as they enable dual electrical–optical functionality that bridges the efficiency of electronics and the bandwidth of photonics. However, efficient, scalable, and CMOS-compatible implementations of electro-optic memristors are still lacking. Here, we devise electro-optic memristors by structuring the phase-change material as a nanoscale constriction, geometrically confining the electrically generated heat profile to overlap with the optical field, thus achieving programmability and readability in both the electrical and optical domains. We demonstrate sub-10 pJ electrical switching energy and a high electro-optical modulation efficiency of 0.15 nJ/dB. Our work opens up opportunities for high-performance and energy-efficient integrated electro-optic neuromorphic computing.