A compact model able to predict the electrical read-out of field-effect biosensors based on two-dimensional (2D) semiconductors is introduced. It comprises the analytical description of the electrostatics including the charge density in the 2D semiconductor, the site-binding modeling of the barrier oxide surface charge, and the Stern layer plus an ion-permeable membrane, all coupled with the carrier transport inside the biosensor and solved by making use of the Donnan potential inside the ion-permeable membrane formed by charged macromolecules. This electrostatics and transport description account for the main surface-related physical and chemical processes that impact the biosensor electrical performance, including the transport along the low-dimensional channel in the diffusive regime, electrolyte screening, and the impact of biological charges. The model is implemented in Verilog-A and can be employed on standard circuit design tools. The theoretical predictions obtained with the model are validated against measurements of a MoS2 field-effect biosensor for streptavidin detection showing excellent agreement in all operation regimes and leading the way for the circuit-level simulation of biosensors based on 2D semiconductors.