Two-dimensional (2D) transition metal dichalcogenides (TMDCs) are highly promising nanomaterials for various electronic devices such as field-effect transistors, junction diodes, tunneling devices, and, more recently, memristors. 2D MoSe₂ stands out for having high electrical conductivity, charge carrier mobility, and melting point. While these features make it particularly appropriate as a switching layer in memristive devices, reliable and scalable production of large-area 2D MoSe₂ still represents a challenge. In this study, we manufacture 2D MoSe₂ films by atmospheric-pressure chemical vapor deposition and investigate them on the atomic scale. We selected and transferred MoSe₂ bilayer to serve as a switching layer between asymmetric Au–Cu electrodes in miniaturized crossbar vertical memristors. The electrochemical metallization devices showed forming-free, bipolar resistive switching at low voltages, with clearly identifiable nonvolatile states. Other than low-power neuromorphic computing, low switching voltages approaching the range of biological action potentials could unlock hybrid biological interfaces.