Copper interconnects in modern integrated circuits require ultra-thin barriers to prevent intermixing of Cu with surrounding dielectric materials. Conventional barriers rely on metals like TaN, however their finite thickness reduces the cross-sectional area and significantly increases the resistivity of nanoscale interconnects. In this study, a new class of two-dimensional (2D) Cu diffusion barriers, hexagonal boron nitride (h-BN) and molybdenum disulfide (MoS2), is demonstrated for the first time. Using time-dependent dielectric breakdown measurements and scanning transmission electron microscopy coupled with energy dispersive X-ray spectroscopy and electron energy loss spectroscopy, these 2D materials are shown to be promising barrier solutions for ultra-scaled interconnect technology. The predicted lifetime of devices with directly deposited 2D barriers can achieve three orders of magnitude improvement compared to control devices without barriers.