In this work we report about the derivation of a physics-based compact model of Random Telegraph Noise (RTN) in HfO2-based Resistive Random Access Memory (RRAM) devices. Starting from the physics of charge transport, which is different in the high and low resistive states (HRS and LRS), we explore the mechanisms responsible for RTN exploiting a hybrid approach, based on self-consistent physics simulations and geometrical simplifications. Then, we develop a simple yet effective physics-based compact model of RTN valid in both states, which can be steadily integrated in state-of-the-art RRAM compact models. The RTN compact model predictions are validated by comparison with both a large experimental dataset obtained by measuring RRAM devices in different conditions, and data reported in the literature. In addition, we show how the model enables advanced circuit simulations by exploring three different circuits for memory, security, and logic applications.