The fabrication of integrated circuits (ICs) employing two-dimensional (2D) materials is a major goal of semiconductor industry for the next decade, as it may allow the extension of the Moore’s law, aids in in-memory computing and enables the fabrication of advanced devices beyond conventional complementary metal-oxide-semiconductor (CMOS) technology. However, most circuital demonstrations so far utilizing 2D materials employ methods such as mechanical exfoliation that are not up-scalable for wafer-level fabrication, and their application could achieve only simple functionalities such as logic gates. Here, we present the fabrication of a crossbar array of memristors using multilayer hexagonal boron nitride (h-BN) as dielectric, that exhibit analog bipolar resistive switching in >96% of devices, which is ideal for the implementation of multi-state memory element in most of the neural networks, edge computing and machine learning applications. Instead of only using this memristive crossbar array to solve a simple logical problem, here we go a step beyond and present the combination of this h-BN crossbar array with CMOS circuitry to implement extreme learning machine (ELM) algorithm. The CMOS circuit is used to design the encoder unit, and a h-BN crossbar array of 2D hexagonal boron nitride (h-BN) based memristors is used to implement the decoder functionality. The proposed hybrid architecture is demonstrated for complex audio, image, and other non-linear classification tasks on real-time datasets.