Memristive in-memory computing offers a promising pathway to overcome the von Neumann bottleneck, yet the lack of computationally efficient compact memristor models that simultaneously capture dynamic accuracy and inherent variability remains often a barrier to large-scale circuit design. This work presents a variability-aware physics-based compact model for HfO2 ReRAM devices fabricated in 130 nm 1T1R CMOS technology. The conduction term combines two transport mechanisms to achieve high accuracy in the low-voltage range, which is essential for inference operations in AI. The state dynamic mobility ranges over thirty orders of magnitude simulating the filament formation. To address cycle-to-cycle variability, the model is described by a stochastic differential equation formulation introducing Gaussian fluctuations to the activation energy barrier which reproduces the variability characteristics observed in potentiation and depression measurements. Validated against experimental quasi-static and pulse data, this model addresses the challenge of balancing between high-fidelity physical simulations and efficient EDA-compatible circuit-level design, enabling robust verification of neuromorphic architectures within standard CAD workflows.