<p>Memristors are an emerging component in digital design applications. Non-volatile nature, simple structure, fast switching speed, and pinch hysteresis current–voltage characteristics that are the major driving attributes of the memristor. A variety of memristor structures and materials lead to different types of electrical switching behavior, i.e., bipolar and unipolar. In the literature, existing models address both unipolar and bipolar behavior. However, a computationally efficient and accurate unified model is needed that simulates the behavior of both types of devices to simulate and predict the behavior of the memristor in different circuits and systems. The modeling parameters are calibrated to fit accurately to both bipolar and unipolar memristive devices. The proposed model can optimize the computational complexity and accuracy by hyper-tuning the experimental fitting parameters. The compact unified model is validated against two physical memristive devices, i.e., bipolar (Pt–TiO<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mrow /> <mn>2</mn> <mrow /> </mmultiscripts> </math></EquationSource> </InlineEquation>–Pt) and unipolar (Pt–ZnO–Pt) memristors. The proposed model improves simulation run-time by up to 8.21% and reduces the relative root mean squared error by 12.94%. This will pave the way for the circuit design industry to use the generic unified memristor model for circuit applications.</p>