In the present work, a rigorous two-dimensional physical simulator is developed to characterize the operation and to optimize the structure of a highly sensitive linear 2D MOSFET magnetic sensor. The magnetic field equation and the carrier transport equations are efficiently coupled and accurately solved to determine the effects of external applied magnetic field on the electrical characteristics of the MOSFET based sensor. The accuracy of the present simulator is tested for different device and circuit parameters to allow the use of it as an efficient CAD tool to fully characterize smart two-directions MOSFET magnetic sensor.