Integrated nanoelectromechanical (NEM) relays can be used instead of transistors to implement ultra-low power logic circuits, due to their abrupt turn-off characteristics and zero off-state leakage. Further, realizing circuits with 4-terminal (4-T) NEM relays enables significant reduction in circuit device count compared to conventional transistor circuits. For practical 4-T NEM circuits, however, the relays need to be miniaturized and integrated with high-density back-end-of-line (BEOL) interconnects, which is challenging and has not been realized to date. Here, we present electrostatically actuated silicon 4-T NEM relays that are integrated with multi-layer BEOL metal interconnects, implemented using a commercial silicon-on-insulator (SOI) foundry process. We demonstrate 4-T switching and the use of body-biasing to reduce pull-in voltage of a relay with a 300 nm airgap, from 15.8 V to 7.8 V, consistent with predictions of the finite-element model. Our 4-T NEM relay technology enables new possibilities for realizing NEM-based circuits for applications demanding harsh environment computation and zero standby power, in industries such as automotive, Internet-of-Things, and aerospace.